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

1,2

Comments

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

Links

Table of n, a(n) for n=1..21.

David A. Corneth, PARI program for some upper bounds below specified value

David A. Corneth, Upper bounds (or actual values) for a(n)

Prog

(PARI) 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

Crossrefs

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

Sequence in context: A286876 A181702 A304890 * A241254 A007372 A062910

Adjacent sequences: A264152 A264153 A264154 * A264156 A264157 A264158

Keyword

nonn,more

Author

Michel Marcus, Nov 06 2015

Status

approved