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 A123856 Primes p that divide A123855(p-1). 7
 2, 3, 5, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 181, 197, 211, 223, 227, 229, 269, 317, 337, 349, 353, 379, 383, 389, 401, 421, 439, 449, 457, 463, 479, 521, 523, 541, 547, 563, 569, 571, 587, 599, 613, 617, 631, 643 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A123855(n) = Sum_{j=1..n} Sum_{i=1..n} prime(i)^j. Prime p = a(n) divides A123855(p-1). Nonprime numbers n that divide A123855(n-1) are listed in A123857. It appears that 2^k divides A123855(2^k-1) for all k>0 (confirmed for 01 then p:=nextprime( procname(n-1)) else p:=2 fi: while A123855_mod(p-1, p)<>0 do p:=nextprime( p ) od: p end; # M. F. Hasler, Nov 10 2006 MATHEMATICA fQ[p_] := Mod[ Sum[ PowerMod[ Prime@ i, j, p], {j, p - 1}, {i, p - 1}], p] == 0; Select[ Prime@ Range@ 117, fQ] (* Robert G. Wilson v, Jun 10 2011 *) CROSSREFS Cf. A123857, A123855, A086787. Sequence in context: A215799 A237057 A183073 * A120857 A233516 A000043 Adjacent sequences:  A123853 A123854 A123855 * A123857 A123858 A123859 KEYWORD nonn AUTHOR Alexander Adamchuk, Oct 13 2006 STATUS approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)