A278315 Composite numbers k such that sum of proper divisors of k divides 2^k-1.

4, 16, 18, 125, 144, 256, 400, 6489, 27559, 42601, 65536, 105800, 110825, 128975, 129600, 145800, 152775, 200025, 208679, 213444, 226033, 298116, 435600, 649800, 761959, 892561, 1076647, 1248961, 1622225, 1851569, 2059175, 2443575, 2668050, 3612672, 3967223, 7890199, 7947833

Offset

1,1

Comments

From Robert Israel, Nov 18 2016: (Start)

Contains A001146 except for 2.

Each even term is a square or twice a square.

No odd terms are squares. (End)

Links

Amiram Eldar, Table of n, a(n) for n = 1..130

Example

18 is a term because A001065(18) = 21 divides 2^18-1.

Maple

select(p -> not(isprime(p)) and 2 &^ p mod (numtheory:-sigma(p) - p) = 1, [$4..10^5]); # Robert Israel, Nov 18 2016

Mathematica

Select[Range[8*10^6], CompositeQ[#]&&PowerMod[2, #, DivisorSigma[1, #]-#] == 1&] (* Harvey P. Dale, Jul 31 2018 *)

Prog

(PARI) is(n)=Mod(2, sigma(n)-n)^n==1 && !isprime(n);

Crossrefs

Cf. A000225, A001065, A001146.

Sequence in context: A117102 A077476 A282552 * A175527 A146510 A232524

Adjacent sequences: A278312 A278313 A278314 * A278316 A278317 A278318

Keyword

nonn

Author

Altug Alkan, Nov 18 2016

Status

approved