%I #15 Apr 23 2019 09:17:26
%S 24,12,8,6,120,4,168,3,216,60,264,2,312,84,40,384,408,108,456,30,56,
%T 132,552,1,600,156,72,42,696,20,744,192,88,204,840,54,888,228,104,15,
%U 984,28,1032,66,1080,276,1128,128,1176,300,136,78,1272,36,1320,21,152,348,1416,10
%N Row 24 of array in A059897.
%C Also column 24 of A059897.
%C A self-inverse permutation of the positive integers with no fixed points; a composition of A073675, A120229 and A120230.
%C 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.
%H Peter Munn, <a href="/A307267/b307267.txt">Table of n, a(n) for n = 1..5120</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = A059897(24,n) = A059897(n,24).
%F a(n) = A073675(A120229(A120230(n))) = A073675(n) * A120229(n) * A120230(n) / n^2.
%o (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])))); }
%o a(n) = T(n, 24); \\ _Michel Marcus_, Apr 23 2019
%Y Cf. A059897, A073675, A120229, A120230, A307266.
%K nonn
%O 1,1
%A _Peter Munn_, Apr 01 2019