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 A277286 Composite numbers k such that b^k == b (mod sigma(k)) for every integer b. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 28 19:06 EST 2023. Contains 367419 sequences. (Running on oeis4.)