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URL: https://oeis.org/A295483

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A295483
Composite squarefree numbers k such that Sum_{i=1..j} (p_i)^k mod k = 0, where p_i is one of the j prime divisors of k.
0
290, 610, 1491, 24423, 55210, 738507, 3619317, 3668889, 384199202, 1307828445, 4664465273
OFFSET
1,1
COMMENTS
Primes are excluded because they are a banal solution of the congruence.
EXAMPLE
Prime factors of 290 are 2, 5, 29 and (2^290 + 5^290 + 29^290) mod 290 = 0.
MAPLE
with(numtheory): P:=proc(q) local a, k, n; for n from 2 to q do
if issqrfree(n) and not isprime(n) then a:=ifactors(n)[2];
if add(a[k][1]^n, k=1..nops(a)) mod n = 0 then print(n); fi; fi; od; end: P(10^6);
MATHEMATICA
okQ[k_] := Module[{pp, ee}, {pp, ee} = FactorInteger[k] // Transpose; Max[ee] < 2 && Mod[Total[PowerMod[#, k, k]& /@ pp], k] == 0]; Reap[For[k = 6, k < 4*10^6, k++, If[CompositeQ[k], If[okQ[k], Print[k]; Sow[k] ] ] ] ][[2, 1]] (* Jean-François Alcover, Feb 15 2018 *)
PROG
(PARI) lista(nn) = {forcomposite(n=1, nn, if (issquarefree(n), f = factor(n); s = sum(k=1, #f~, Mod(f[k, 1], n)^n); if (lift(s) == 0, print1(n, ", ")); ); ); } \\ Michel Marcus, Feb 13 2018
CROSSREFS
Subsequence of A120944.
Sequence in context: A296055 A090839 A158255 * A075299 A031712 A251049
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Feb 13 2018
EXTENSIONS
a(6)-a(8) from Michel Marcus, Feb 13 2018
a(9)-a(11) from Giovanni Resta, Feb 13 2018
STATUS
approved