A277286 Composite numbers k such that b^k == b (mod sigma(k)) for every integer b.

7381, 13357, 18421, 69121, 70021, 129961, 192589, 241501, 271921, 313501, 342793, 399421, 423613, 625681, 780913, 1265641, 1362097, 1501489, 1566181, 1673101, 1691521, 1728001, 2228941, 2381401, 2472301, 2642221, 3156661, 3171961, 3383281, 3557521, 3730321, 4033861, 4233061, 4831201, 5387041, 6720961

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Maple

N:= 10^7: # to get all terms <= N
Q:= select(isprime, [seq(q, q=5..N/9, 4)]):
filter:= proc(n) local s; uses numtheory;
  s:= sigma(n);
  issqrfree(s) and andmap(p -> (n-1 mod (p-1) = 0), factorset(s));
end proc:
select(filter, {seq(seq(q*m^2, m = 3..floor(sqrt(N/q)), 2), q=[1, op(Q)])}); # Robert Israel, Sep 21 2016

Mathematica

M = 10^7; (* to get all terms <= M *)
Q = Select[Range[5, M/9, 4], PrimeQ];
filter[n_] := Module[{s = DivisorSigma[1, n]}, SquareFreeQ[s] && AllTrue[FactorInteger[s][[All, 1]], Mod[n-1, #-1] == 0&]];
Select[Union@Flatten[Table[Table[q*m^2, {m, 3, Floor[Sqrt[M/q]], 2}], {q, Prepend[Q, 1]}]], filter] (* Jean-François Alcover, May 24 2023, after Robert Israel *)

Crossrefs

Cf. A002808, A000203.

Sequence in context: A043589 A043806 A043824 * A328663 A022255 A189504

Adjacent sequences: A277283 A277284 A277285 * A277287 A277288 A277289

Keyword

nonn

Author

Altug Alkan, Oct 09 2016

Status

approved