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

1,2

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

Links

Table of n, a(n) for n=1..26.

Example

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

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 *)

Crossrefs

Cf. A066135, A066284, A066289-A066292.

Cf. A118076.

Sequence in context: A039499 A341128 A055712 * A260703 A044254 A044635

Adjacent sequences: A066289 A066290 A066291 * A066293 A066294 A066295

Keyword

nonn

Author

Labos Elemer, Dec 12 2001

Extensions

Edited by T. D. Noe, Apr 11 2006

Status

approved