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

%I A105119 #20 Apr 19 2016 01:07:35
%S A105119 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,
%T A105119 27,98,29,30,31,32,33,34,35,36,37,38,39,250,41,42,43,242,75,46,47,162,
%U A105119 49,20,51,338,53,24,55,686,57,58,59,90,61,62,147,64,65,66,67,578,69,70
%N A105119 Numbers obtained by rotating right the indices in the prime signature of n.
%C A105119 If n = p^a*q^b*r^c, then a(n) = p^c*q^a*r^b.
%C A105119 If n = p^a*q^b*r^c*s^d, then a(n) = p^d*q^a*r^b*s^c.
%C A105119 The sequence is a permutation of the positive integers. The first term which is different from A069799 is a(60).
%C A105119 Inverse permutation to A225891. The fixed points are A072774 (squarefree numbers and their powers). - _Ivan Neretin_, Jul 26 2015
%H A105119 Ivan Neretin, <a href="/A105119/b105119.txt">Table of n, a(n) for n = 1..10000</a>
%H A105119 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A105119 a(60) = a(2^2*3*5) = 2*3^2*5 = 90.
%p A105119 f:= proc(n) local F,j,m;
%p A105119       F:= ifactors(n)[2];
%p A105119       m:= nops(F);
%p A105119       mul(F[i,1]^F[i-1,2],i=2..m)*F[1,1]^F[m,2] ;
%p A105119 end proc:
%p A105119 f(1):= 1:
%p A105119 map(f, [$1..100]); # _Robert Israel_, Jul 26 2015
%t A105119 Table[Times @@ ((ar = Transpose[FactorInteger[n]])[[1]]^RotateRight[ar[[2]]]), {n, 70}] (* _Ivan Neretin_, Jul 26 2015 *)
%o A105119 (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 */
%Y A105119 Permutation of A000027(n). Cf. A069799.
%K A105119 nonn
%O A105119 1,2
%A A105119 _Yasutoshi Kohmoto_, Apr 08 2005
%E A105119 Edited by _Ralf Stephan_, Apr 05 2009
%E A105119 a(1)=1 prepended by _Ivan Neretin_, Jul 26 2015