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.

1, 84, 156, 364, 1092, 435708, 986076, 1118480, 1441188, 1674036, 2446668, 2597868, 3108924, 3875508, 4150692, 5537196, 6066396, 6686316, 13729212, 14639436, 18735444, 23307732, 27092052, 31806684, 58266468, 69728724

Offset: 1

Author

Labos Elemer, Dec 12 2001

Keywords

• nonn

Comments

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

Examples

			n=84 is here because 84 divides each one of sigma_4(n)=53771172, sigma_8(n)=2488859101224132, sigma_16(n)=6144339637187846520573009496452, etc.
		

Crossrefs

Cf. A066135, A066284, A066289-A066292.

Cf. A118076.

Programs

Mathematica

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 *)

Extensions

Edited by T. D. Noe, Apr 11 2006