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 A066135 a(n) = least number m > 1 such that sigma_n(m) = k*m for some k. 10
 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 194, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 228, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 194, 6, 10, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) <= 2p, where p = A002586(n) is the smallest prime factor of (1 + 2^n). (Proof. Since sigma_n(2p) = (1 + 2^n)(1 + p^n) and p is odd, 2p divides sigma_n(2p).) - Jonathan Sondow, Nov 23 2012 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA Sum{d^n} = ka(n), d runs over the divisors of a(n), where k is an integer and a(n) is the smallest suitable number. MATHEMATICA Table[m = 2; While[Mod[DivisorSigma[n, m], m] > 0, m++]; m, {n, 100}] (* T. D. Noe, Nov 23 2012 *) CROSSREFS Cf. A000203, A001157, A001158, A001159, A002586, A007691, A046762-A046764, A055709-A055717. Cf. A218860, A218861 (unique values and where they first occur). Sequence in context: A247270 A010726 A084365 * A070393 A071630 A003862 Adjacent sequences:  A066132 A066133 A066134 * A066136 A066137 A066138 KEYWORD nonn AUTHOR Labos Elemer, Dec 06 2001 EXTENSIONS Definition and formulas corrected by Jonathan Sondow, Nov 23 2012 STATUS approved

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Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)