A264154 -id:A264154 - cp's OEIS frontend

A264155 a(n) is the smallest integer m such that n is the least exponent k satisfying sigma(m)^k divides m.

1, 24, 40, 384, 486, 6144, 640, 18688, 39366, 91136, 10240, 23482368, 958464, 52612659, 163840, 375717888, 9568256, 1502871552, 2621440, 353370112, 186646528

Offset: 1

Michel Marcus, Nov 06 2015

Conjecture: for n > 1, a(n) is of the form 2^n * m generally, sometimes of the form 3^n * m, and sometimes of the form 2^(n-1) * m, depending on sigma(m). Upper bounds are mostly of the form 2^n * m for odd m. For example, a(27) <= 2^27 * 5. - David A. Corneth, Feb 14 2019

David A. Corneth, PARI program for some upper bounds below specified value
David A. Corneth, Upper bounds (or actual values) for a(n)

Cf. A000203 (sigma), A007947 (rad), A175200, A264154.

fk(s, m) = {my(j = 1); while(denominator(s^j/m) != 1, j++); j;}
rad(n) = factorback(factorint(n)[, 1]);
a(n) = {my(k = 1, ok = 0, sk); while (!ok, sk = sigma(k); if ((denominator(sk/rad(k)) == 1) && (fk(sk, k) == n), ok = 1, k++; ); ); k; } \\ corrected by Michel Marcus, Feb 14 2019

cp's OEIS Frontend

A264155 a(n) is the smallest integer m such that n is the least exponent k satisfying sigma(m)^k divides m.

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