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

Author

Michel Marcus, Nov 06 2015

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000203 (sigma(n)), A007947 (rad(n)), A175200.

Programs

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, ", ");););}