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A105119 Numbers obtained by rotating right the indices in the prime signature of n. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)