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 A264155 a(n) is the smallest integer m such that n is the least exponent k satisfying sigma(m)^k divides m. 1
 1, 24, 40, 384, 486, 6144, 640, 18688, 39366, 91136, 10240, 23482368, 958464, 52612659, 163840, 375717888, 9568256, 1502871552, 2621440, 353370112, 186646528 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified November 13 01:54 EST 2019. Contains 329085 sequences. (Running on oeis4.)