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.

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

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