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My OEIS published integer sequences

  1. A352881 SeqDB a(n) is the minimal number z having the largest number of solutions to the Diophantine equation 1/z = 1/x + 1/y such that 1 <= x <= y <= 10^n.

  2. A347105 SeqDB a(n) is the greatest sum of the digital roots of the individual factorizations of n.

  3. A355069 SeqDB a(n) is the number of solutions to x^y == y^x (mod p) where 0 < x,y <= p^2 - p and p is the n-th prime.

  4. A355419 SeqDB a(n) is the number of solutions to x^y == y^x (mod p) where 0 < x,y <= p and p is the n-th prime.

  5. A355486 SeqDB a(n) is the number of total solutions (minus the n-th prime) to x^y == y^x (mod p) where 0 < x,y <= p and p is the n-th prime.

  6. A357945 SeqDB Numbers k which are not square but D = (b+c)^2 - k is square, where b = floor(sqrt(k)) and c = k - b^2.

  7. A358016 SeqDB For n >= 3, a(n) is the largest k <= n-2 such that k^2 == 1 (mod n).

  8. A357928 SeqDB a(n) is the smallest c for which (s+c)^2-n is a square, where s = floor(sqrt(n)), or -1 if no such c exists.

  9. A358043 SeqDB Numbers k such that phi(k) is a multiple of 8.

  10. A358051 SeqDB Squares k such that phi(k) is a cube.

  11. A359415 SeqDB Numbers k such that phi(k) is a 5-smooth number where phi is the Euler totient function.

  12. A359864 SeqDB a(n) is the number of solutions to the congruence x^y == y^x (mod n) where 0 <= x,y <= n.

  13. A358821 SeqDB a(n) is the largest square dividing n^2-1.

  14. A360760 SeqDB a(n) = n^16 + n^15 + n^2 + 1 (or crc-16-ibm poly).

  15. A361913 SeqDB a(n) is the number of steps in the main loop of the Pollard's rho integer factorization algorithm with x=2, y=2 and g(x)=x^2-1.

  16. A362008 SeqDB Numbers whose Euler's cototient is divisible by 9.

  17. A362961 SeqDB a(n) = Sum_{b=0..floor(sqrt(n)), n-b^2 is square} b.

  18. A363051 SeqDB a(n) = Sum_{b=0..floor(sqrt(n/2)), n-b^2 is square} b.

  19. A362502 SeqDB Least k > 0 such that (floor(sqrt(n*k)) + 1)^2 mod n is a square.

  20. A363612 SeqDB Number of iterations of phi(x) at n needed to reach a square.

  21. A363680 SeqDB Number of iterations of phi(x) at n needed to reach a cube.

  22. A363896 SeqDB Numbers k such that the sum of primes dividing k (with repetition) is equal to Euler's totient function of k.

  23. A363895 SeqDB Floor of the average of the distinct prime factors of n.

  24. A362951 SeqDB a(n) is the Hamming distance between the binary expansions of n and phi(n) where phi is the Euler totient function (A000010).

  25. A364143 SeqDB a(n) is the minimal number of consecutive squares needed to sum to A216446(n)

  26. A364168 SeqDB Numbers that can be written in more than one way in the form (j+2k)^2-(j+k)^2-j^2 with j,k>0.

  27. A364834 SeqDB Sum of positive integers <= n which are multiples of 2 or 5.

  28. A359198 SeqDB Numbers k such that 2*phi(k)-k is a prime, where phi is A000010.

  29. A363583 SeqDB Numbers k such that 2*phi(k)+k is a prime, where phi is A000010.

  30. A365074 SeqDB Numbers k such that k! - k^2 - 1 is prime.

  31. A365617 SeqDB Iterated Pochhammer symbol.

  32. A365628 SeqDB a(n) = binomial(primorial(n), n).

  33. A365749 SeqDB Number of iterations that produce a record high of the digest of the SHA2-256 hash of the empty string.

  34. A366061 SeqDB Numbers of iterations that produce a record low of the digest of the SHA2-256 hash of the empty string.

  35. A365639 SeqDB Numbers k such that k! + k^3 + 1 is prime.

  36. A365686 SeqDB Numbers k such that there exists a pair of integers (m,h) where 1 <= m < floor(sqrt(k)/2) <= h that satisfy Sum_{j=0..m} (k-j)^2 = Sum_{i=1..m} (h+i)^2.

  37. A366160 SeqDB Numbers whose binary expansion is not quasiperiodic.

  38. A364535 SeqDB a(n) is the number of subsets of the first n primes whose sum is not a prime.

  39. A367690 SeqDB Total number of steps of Euclid's GCD algorithm to calculate gcd(x,y) for all pairs x,y in the range 1 <= x,y <= n.

  40. A367892 SeqDB Total number of steps of Euclid's GCD algorithm to calculate gcd(x,y) for all pairs x,y in the range 1 <= y <= x <= n.

  41. A367379 SeqDB a(n) = Sum_{j=1..n} Sum_{i=1..n} (j mod i).

  42. A368275 SeqDB Fibonacci zig-zag function.

  43. A367954 SeqDB Total number of steps of Euclid's GCD algorithm to calculate gcd(x,y) for all pairs x,y in the range 1 <= x < y <= n.

  44. A369802 SeqDB Inversion count of the Eytzinger array layout of n elements.

  45. A369920 SeqDB The private keys for the 32 BTC Bitcoin puzzle.

  46. A370006 SeqDB Steinhaus-Johnson-Trotter rank of the Eytzinger array layout of n elements.

  47. A368783 SeqDB Lexicographic rank of the permutation which is the Eytzinger array layout of n elements.

  48. A369922 SeqDB a(n) = 8n^3 - 6n - 1.

  49. A370879 SeqDB a(n) = 2^nt + 1 where t is the least x such that there exists an r in the range 2 <= r <= x+1 that is coprime to 2^nx + 1 and has multiplicative order 2^n modulo 2^n*x + 1.

  50. A371124 SeqDB a(n) is the least nonnegative integer y such that y^2 = x^2 - k*n for k and x where n > k >= 1 and n > x >= floor(sqrt(n)).

  51. A371531 SeqDB a(n) is the multiplicative order of A053669(n) modulo n.

  52. A372305 SeqDB a(n) = Product_{k=2..n-1} MultiplicativeOrder(k,n) where gcd(k,n)=1.

  53. A372651 SeqDB a(n) is the product of the distinct nonzero quadratic residues of n.

  54. A373286 SeqDB a(n) = Product_{k=1..n} (k^2 mod n if k^2 mod n > 0).

  55. A373194 SeqDB Numbers k such that phi(k) is a Lucas number.

  56. A373461 SeqDB a(n) = s - t where s = ceiling(sqrt(n*i)), t = sqrt(m), and m = s^2 mod n, for the smallest positive integer i for which m is square.

  57. A373879 SeqDB Composite numbers not factorizable using the Pollard-rho algorithm with parameters x=2,y=2 and f(x)=x^2-1.

  58. A373716 SeqDB a(n) is the number of distinct products i*j minus the number of distinct sums i+j with 1 <= i, j <= n.

  59. A373652 SeqDB Composite numbers k for which g = gcd(f(i*c), k) = 1 or k for all i in the range 1 <= i <= c, where f(x) = Product_{j=1..c} x+j and c = floor(k^(1/4)).

  60. A374625 SeqDB In the binary expansion of n, expand bits 1 -> 01 and 0 -> 10.

  61. A374510 SeqDB Sum of those numbers t which have a unique representation as the sum of floor(n/2) distinct squares from among 1^2,...,n^2.

  62. A374730 SeqDB a(n) = n * binomial(floor(log_2(n)) + 1, 2).

  63. A374720 SeqDB Permutation rank of the initial state S of length n in an RC4-like Key Scheduling Algorithm with key comprising numbers 1 to n.

  64. A375156 SeqDB In the binary expansion of n: expand bits 1 -> 01 and 0 -> x0 from most to least significant, where x is the complement of the previous bit from n.

  65. A375109 SeqDB Number of distinct products i*j with 1 <= i, j <= n which are not the sum of two numbers between 1 and n.

  66. A374967 SeqDB a(n) is the Verhoeff check digit of n.

  67. A375585 SeqDB Number of ASCII letter 'A' bytes that when compressed with zlib generate a new record longest compressed byte stream.

  68. A375649 SeqDB Number of comparisons and swaps in the Batcher odd-even merge sort needed to sort n items.

  69. A375764 SeqDB a(n) is the sum of distinct sums of all subsets with two or more elements of {1, 2, ..., n}.

  70. A375825 SeqDB Triangle read by rows where row n is the Eytzinger array layout of n elements (a permutation of {1..n}).

  71. A375745 SeqDB a(n) is the sum of the vector of the reduced discriminant of the n-th cyclotomic polynomial.

  72. A375789 SeqDB First position index for A197123(n) in the decimal expansion of Pi.

  73. A374849 SeqDB In the binary expansion of n: Collapse bits from most to least significant 10 -> 1, 01 -> 0, 00 -> nothing, 11 -> nothing.

  74. A375959 SeqDB Partial products of A006257.

  75. A376295 SeqDB The binary expansion of a(n) is the reversal of the concatenation of the binary expansions of 1,...,n.

  76. A376299 SeqDB Fixed points of A008473.

  77. A376951 SeqDB Characteristic polynomial of the Pappus graph: a(n) = (n-3)n^4(n+3)*(n^2-3)^6.

  78. A377059 SeqDB a(n) is the smallest even r less than n-1 such that x^r = 1 (mod n) for the least x such that gcd(x,n)=1 for n >= 4 else 0.

  79. A377029 SeqDB a(1) = 0; therafter in the binary expansion of a(n-1), expand bits: 1->01 and 0->10.

  80. A376613 SeqDB The binary expansion of a(n) tracks where the merge operations occurs in a Tim sort algorithm applied to n blocks.

  81. A377704 SeqDB a(n) = binomial(Fibonacci(n)+Fibonacci(n+1)-2,Fibonacci(n)-1).

  82. A378298 SeqDB Number of solutions that satisfy the congruence: i^2 == j^2 (mod n) with 1 <= i < j <= n.

  83. A378488 SeqDB Table T(n,k) read by rows where in the n-th row the k-th column is the permutation rank of the k-th solution to the n-queens problem in a n X n board.

  84. A378299 SeqDB Read the binary representation of n from the most to least significant bit then perform a cumulative XOR and store by reading from least to most significant bit.

  85. A379040 SeqDB Fixed points in A379015.

  86. A379015 SeqDB a(n) is the reversed non-adjacent form (NAF) representation of n.

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