|
%I #16 Apr 23 2019 09:17:36
%S 8,4,24,2,40,12,56,1,72,20,88,6,104,28,120,128,136,36,152,10,168,44,
%T 184,3,200,52,216,14,232,60,248,64,264,68,280,18,296,76,312,5,328,84,
%U 344,22,360,92,376,384,392,100,408,26,424,108,440,7,456,116,472,30,488,124,504,32
%N Row 8 of array in A059897.
%C Also column 8 of A059897.
%C A self-inverse permutation of the positive integers with no fixed points; A073675 composed with A120230.
%C 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.
%H Peter Munn, <a href="/A307266/b307266.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(8,n) = A059897(n,8).
%F a(n) = A073675(A120230(n)) = A120230(A073675(n)) = A073675(n) * A120230(n) / n.
%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, 8); \\ _Michel Marcus_, Apr 23 2019
%Y Cf. A059897, A073675, A120230, A307267.
%K nonn
%O 1,1
%A _Peter Munn_, Apr 01 2019
|
