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

1,1

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

Formula

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

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

Prog

(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

Crossrefs

Cf. A059897, A073675, A120229, A120230, A307266.

Sequence in context: A033344 A228437 A079341 * A080865 A040555 A081314

Adjacent sequences: A307264 A307265 A307266 * A307268 A307269 A307270

Keyword

nonn

Author

Peter Munn, Apr 01 2019

Status

approved