A274554 Numbers k such that sigma(k) == 0 (mod k-4).

3, 5, 6, 10, 22, 24, 60, 130, 184, 1012, 2272, 18904, 33664, 70564, 85936, 100804, 391612, 527872, 1090912, 17619844, 2147713024, 6800695312, 34360655872, 549759483904, 1661355408388, 28502765343364, 82994670582016, 99249696661504, 120646991405056, 431202442356004, 952413274955776, 1222508573411584, 36028797958488064, 144141578099802112, 576460756061519872

Offset

1,1

Links

Max Alekseyev, Table of n, a(n) for n = 1..40

Example

sigma(5) mod (5-4) = 6 mod 1 = 0.

Maple

q:= k-> is(irem(numtheory[sigma](k), k-4)=0):
select(q, [$5..400000])[];  # Alois P. Heinz, Jun 14 2025

Mathematica

k = -4; Select[Range[Abs@ k + 1, 10^7], Mod[DivisorSigma[1, #], # + k] == 0 &] (* Michael De Vlieger, Jul 01 2016 *)

Prog

(Magma) [n: n in [5..2*10^6] | SumOfDivisors(n) mod (n-4) eq 0 ]; // Vincenzo Librandi, Jul 02 2016

Crossrefs

Contains subsequences: A125247, 2 times odd terms of A125246, and 6*t for terms t of A056006 with gcd(t,6) = 1 and (sigma(t)+2)/t = 3.

Cf. A067702, A223609, A274551, A274552, A274553, A274566.

Sequence in context: A270416 A290269 A115059 * A250218 A092835 A335403

Adjacent sequences: A274551 A274552 A274553 * A274555 A274556 A274557

Keyword

nonn

Author

Paolo P. Lava, Jun 28 2016

Extensions

a(19)-a(24) from Giovanni Resta, Jul 01 2016

a(1)=3 inserted and a(26)-a(35) added by Max Alekseyev, Oct 13 2025

Status

approved