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

Author

Yasutoshi Kohmoto, Apr 08 2005

Keywords

• nonn

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

Examples

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

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Permutation of A000027(n). Cf. A069799.

Programs

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 *)

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 */

Extensions

Edited by Ralf Stephan, Apr 05 2009

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