A105119 Numbers obtained by rotating right the indices in the prime signature of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 18, 13, 14, 15, 16, 17, 12, 19, 50, 21, 22, 23, 54, 25, 26, 27, 98, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 250, 41, 42, 43, 242, 75, 46, 47, 162, 49, 20, 51, 338, 53, 24, 55, 686, 57, 58, 59, 90, 61, 62, 147, 64, 65, 66, 67, 578, 69, 70

Offset

1,2

Comments

If n = p^a*q^b*r^c, then a(n) = p^c*q^a*r^b.

If n = p^a*q^b*r^c*s^d, then a(n) = p^d*q^a*r^b*s^c.

The sequence is a permutation of the positive integers. The first term which is different from A069799 is a(60).

Inverse permutation to A225891. The fixed points are A072774 (squarefree numbers and their powers). - Ivan Neretin, Jul 26 2015

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Example

a(60) = a(2^2*3*5) = 2*3^2*5 = 90.

Maple

f:= proc(n) local F, j, m;
      F:= ifactors(n)[2];
      m:= nops(F);
      mul(F[i, 1]^F[i-1, 2], i=2..m)*F[1, 1]^F[m, 2] ;
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Jul 26 2015

Mathematica

Table[Times @@ ((ar = Transpose[FactorInteger[n]])[[1]]^RotateRight[ar[[2]]]), {n, 70}] (* Ivan Neretin, Jul 26 2015 *)

Prog

(PARI) a(n)=local(m, s); m=factor(n); s=matsize(m)[1]; prod(i=2, s, m[i, 1]^m[i-1, 2])*m[1, 1]^m[s, 2] /* Ralf Stephan, Apr 05 2009 */

Crossrefs

Permutation of A000027(n). Cf. A069799.

Sequence in context: A254650 A032994 A072356 * A069799 A225891 A295417

Adjacent sequences: A105116 A105117 A105118 * A105120 A105121 A105122

Keyword

nonn

Author

Yasutoshi Kohmoto, Apr 08 2005

Extensions

Edited by Ralf Stephan, Apr 05 2009

a(1)=1 prepended by Ivan Neretin, Jul 26 2015

Status

approved