

A264154


For numbers m such that rad(n) divides sigma(n), this sequence gives the minimum exponent k such that sigma(m)^k divides m.


2



1, 1, 2, 1, 3, 3, 3, 1, 3, 3, 2, 2, 2, 3, 4, 5, 1, 3, 2, 2, 7, 1, 2, 4, 3, 3, 2, 3, 3, 2, 5, 2, 2, 3, 3, 5, 2, 3, 7, 3, 3, 3, 5, 3, 4, 2, 5, 3, 2, 7, 2, 3, 3, 3, 5, 2, 7, 2, 6, 2, 5, 3, 2, 3, 3, 2, 3, 1, 3, 3, 4, 3, 11, 4, 7, 3, 2, 2, 5, 3, 3, 5, 3, 4, 4, 7, 4
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OFFSET

1,3


LINKS

Michel Marcus, Table of n, a(n) for n = 1..10000


EXAMPLE

A175200(2) is 6, and for 6, sigma(6)^k/6 is already an integer with k=1, so a(2)=6.
A175200(3) is 24, and for 24, sigma(24)/24 is not an integer while sigma(24)^2/24 is an integer, so a(3)=2.


PROG

(PARI) fk(s, m) = {j = 1; while(denominator(s^j/m) != 1, j++); j; }
rad(n) = factorback(factorint(n)[, 1]);
lista(nn) = {for (n=1, nn, if (denominator(sigma(n)/rad(n)) == 1, k = fk(sigma(n), n); print1(k, ", "); ); ); }


CROSSREFS

Cf. A000203 (sigma(n)), A007947 (rad(n)), A175200.
Sequence in context: A124770 A334300 A308093 * A302641 A099246 A303119
Adjacent sequences: A264151 A264152 A264153 * A264155 A264156 A264157


KEYWORD

nonn


AUTHOR

Michel Marcus, Nov 06 2015


STATUS

approved



