cp's OEIS Frontend

A066292 Numbers n such that n divides sigma_(2^k)(n), the sum of the 2^k powers of the divisors of n, for all k>1.

%I A066292 #9 Aug 20 2021 22:49:05
%S A066292 1,84,156,364,1092,435708,986076,1118480,1441188,1674036,2446668,
%T A066292 2597868,3108924,3875508,4150692,5537196,6066396,6686316,13729212,
%U A066292 14639436,18735444,23307732,27092052,31806684,58266468,69728724
%N A066292 Numbers n such that n divides sigma_(2^k)(n), the sum of the 2^k powers of the divisors of n, for all k>1.
%C A066292 Let d be the vector of divisors of n. The sequence d^(2^k) mod n has some period p. Thus if n divides sigma_(2^k)(n) for one period, then n divides sigma_(2^k)(n) for all k. For these n, the first period ends for k < 158. Hence it is easy to verify divisibility for all k. - _T. D. Noe_, Apr 11 2006
%e A066292 n=84 is here because 84 divides each one of sigma_4(n)=53771172, sigma_8(n)=2488859101224132, sigma_16(n)=6144339637187846520573009496452, etc.
%t A066292 t={}; Do[If[Mod[DivisorSigma[4,n],n]==0, AppendTo[t,n]], {n,10^8}]; Do[t=Select[t,Mod[DivisorSigma[2^k,# ],# ]==0&],{k,3,20}]; t (* _T. D. Noe_, Apr 11 2006 *)
%Y A066292 Cf. A066135, A066284, A066289-A066292.
%Y A066292 Cf. A118076.
%K A066292 nonn
%O A066292 1,2
%A A066292 _Labos Elemer_, Dec 12 2001
%E A066292 Edited by _T. D. Noe_, Apr 11 2006