# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a264155 Showing 1-1 of 1 %I A264155 #24 Sep 01 2019 22:08:19 %S A264155 1,24,40,384,486,6144,640,18688,39366,91136,10240,23482368,958464, %T A264155 52612659,163840,375717888,9568256,1502871552,2621440,353370112, %U A264155 186646528 %N A264155 a(n) is the smallest integer m such that n is the least exponent k satisfying sigma(m)^k divides m. %C A264155 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 A264155 David A. Corneth, PARI program for some upper bounds below specified value %H A264155 David A. Corneth, Upper bounds (or actual values) for a(n) %o A264155 (PARI) fk(s, m) = {my(j = 1); while(denominator(s^j/m) != 1, j++); j;} %o A264155 rad(n) = factorback(factorint(n)[, 1]); %o A264155 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 A264155 Cf. A000203 (sigma), A007947 (rad), A175200, A264154. %K A264155 nonn,more %O A264155 1,2 %A A264155 _Michel Marcus_, Nov 06 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE