%I #24 Sep 01 2019 22:08:19

%S 1,24,40,384,486,6144,640,18688,39366,91136,10240,23482368,958464,

%T 52612659,163840,375717888,9568256,1502871552,2621440,353370112,

%U 186646528

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

%C 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

%H David A. Corneth, <a href="/A264155/a264155.gp.txt">PARI program for some upper bounds below specified value</a>

%H David A. Corneth, <a href="/A264155/a264155.txt">Upper bounds (or actual values) for a(n)</a>

%o (PARI) fk(s, m) = {my(j = 1); while(denominator(s^j/m) != 1, j++); j;}

%o rad(n) = factorback(factorint(n)[, 1]);

%o 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

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

%K nonn,more

%O 1,2

%A _Michel Marcus_, Nov 06 2015