A123856 Primes p that divide A123855(p-1).

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

Offset: 1

Author

Alexander Adamchuk, Oct 13 2006

Keywords

• nonn

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 0

Links

• M. F. Hasler, Nov 10 2006, Table of n, a(n) for n = 1..199

Crossrefs

Cf. A123857, A123855, A086787.

Programs

Maple

A123855_mod := proc(n,p) option remember; local s,i,pi; s:=0: for i to n do pi:= ithprime(i) mod p: if pi=1 then s:=s+n mod p: else s := s+pi*(pi &^ n - 1)/(pi-1) mod p fi od end; A123856 := proc(n::posint) option remember; local p; if n>1 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 *)

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