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A105119 Numbers obtained by rotating right the indices in the prime signature of n. 6
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
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
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 March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)