cp's OEIS Frontend

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

%I A066135 #29 Dec 18 2018 17:02:48
%S A066135 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,
%T A066135 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,
%U A066135 6,84,6,10,6,34,6,10,6,84,6,10,6,34,6,10,6,194,6,10,6
%N A066135 a(n) = least number m > 1 such that sigma_n(m) = k*m for some k.
%C A066135 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
%H A066135 T. D. Noe, <a href="/A066135/b066135.txt">Table of n, a(n) for n = 1..10000</a>
%F A066135 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.
%t A066135 Table[m = 2; While[Mod[DivisorSigma[n, m], m] > 0, m++]; m, {n, 100}] (* _T. D. Noe_, Nov 23 2012 *)
%Y A066135 Cf. A000203, A001157, A001158, A001159, A002586, A007691, A046762-A046764, A055709-A055717.
%Y A066135 Cf. A218860, A218861 (unique values and where they first occur).
%K A066135 nonn
%O A066135 1,1
%A A066135 _Labos Elemer_, Dec 06 2001
%E A066135 Definition and formulas corrected by _Jonathan Sondow_, Nov 23 2012