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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 16 06:48 EST 2021. Contains 340204 sequences. (Running on oeis4.)