A307266 Row 8 of array in A059897.

8, 4, 24, 2, 40, 12, 56, 1, 72, 20, 88, 6, 104, 28, 120, 128, 136, 36, 152, 10, 168, 44, 184, 3, 200, 52, 216, 14, 232, 60, 248, 64, 264, 68, 280, 18, 296, 76, 312, 5, 328, 84, 344, 22, 360, 92, 376, 384, 392, 100, 408, 26, 424, 108, 440, 7, 456, 116, 472, 30, 488, 124, 504, 32

Offset: 1

Author

Peter Munn, Apr 01 2019

Keywords

• nonn

Comments

Also column 8 of A059897.

A self-inverse permutation of the positive integers with no fixed points; A073675 composed with A120230.

The permutation swaps pairs of integers whose ratio is 1:8 or 1:2, these ratios corresponding to the factorizations 1*8 = 2*4 = 8.

Links

• Peter Munn, Table of n, a(n) for n = 1..5120
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A059897, A073675, A120230, A307267.

Programs

PARI

T(n, k) = {if (n==1, return (k)); if (k==1, return (n)); my(fn=factor(n), fk=factor(k)); vp = setunion(fn[, 1]~, fk[, 1]~); prod(i=1, #vp, vp[i]^(bitxor(valuation(n, vp[i]), valuation(k, vp[i])))); }
a(n) = T(n, 8); \\ Michel Marcus, Apr 23 2019

Formula

a(n) = A059897(8,n) = A059897(n,8).

a(n) = A073675(A120230(n)) = A120230(A073675(n)) = A073675(n) * A120230(n) / n.