A066135 a(n) = least number m > 1 such that sigma_n(m) = k*m for some k.

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

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 A334937

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