A307267 Row 24 of array in A059897.

24, 12, 8, 6, 120, 4, 168, 3, 216, 60, 264, 2, 312, 84, 40, 384, 408, 108, 456, 30, 56, 132, 552, 1, 600, 156, 72, 42, 696, 20, 744, 192, 88, 204, 840, 54, 888, 228, 104, 15, 984, 28, 1032, 66, 1080, 276, 1128, 128, 1176, 300, 136, 78, 1272, 36, 1320, 21, 152, 348, 1416, 10

Offset: 1

Author

Peter Munn, Apr 01 2019

Keywords

• nonn

Comments

Also column 24 of A059897.

A self-inverse permutation of the positive integers with no fixed points; a composition of A073675, A120229 and A120230.

The permutation swaps pairs of integers whose ratio is 1:24, 1:6, 3:8 or 2:3, these ratios corresponding to the factorizations 1*24 = 2*12 = 3*8 = 4*6 = 24. Row 24 is the first row of A059897 to exhibit more than 2 such ratios.

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, A120229, A120230, A307266.

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, 24); \\ Michel Marcus, Apr 23 2019

Formula

a(n) = A059897(24,n) = A059897(n,24).

a(n) = A073675(A120229(A120230(n))) = A073675(n) * A120229(n) * A120230(n) / n^2.