|
| |
|
|
A118076
|
|
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>0.
|
|
2
| | |
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Although these numbers have been tested up to k=20, it is conjectured that n divides sigma_(2^k)(n) for all k>0. Intersection of A046762 and 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<14. Hence it is easy to verify divisibility for all k. Intersection of A046762 and A066292. - T. D. Noe (noe(AT)sspectra.com), Apr 12 2006
|
|
|
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[2, n], n]==0, AppendTo[t, n]], {n, 10^8}]; Do[t=Select[t, Mod[DivisorSigma[2^k, # ], # ]==0&], {k, 2, 20}]; t
|
|
|
CROSSREFS
| Cf. A076230 (n divides sigma_2(n) and sigma_4(n)).
Sequence in context: A203093 A202580 A076230 * A056746 A111194 A096132
Adjacent sequences: A118073 A118074 A118075 * A118077 A118078 A118079
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Apr 11 2006
|
| |
|
|
