A124273 Primes p that divide A124271(p) = Sum_{i=1..p} (prime(i)^p - 1) / (prime(i) - 1).

3, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 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, 647, 677

Offset: 1

Author

Alexander Adamchuk, Oct 23 2006

Keywords

• nonn

Comments

a(n) almost coincides with A123856(n). Up to 1000 there are only 3 terms of A123856(n) that are different from the terms of a(n), see A124275.

Links

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

Crossrefs

Cf. A123856, A124271, A124274 (nonprimes n that divide A124271(n)), A124275 (terms of A123856 that are not in this sequence).

Programs

Maple

A124271_mod:=proc(n) option remember; local s,i,p; s:=0: for i to n do p:=ithprime(i) mod n: if p<>1 then s:=s+(p&^n - 1)/(p - 1) mod p fi od:s end; A124273 := proc(n::posint) option remember; local p; if n>1 then p:=nextprime( procname(n-1)) else p:=2 fi: while A124271_mod(p)<>0 do p:=nextprime( p ) od: p end # M. F. Hasler, Nov 10 2006

Mathematica

Select[Prime@ Range@ 125, Divisible[Sum[(Prime[i]^# - 1)/(Prime[i] - 1), {i, 1, #}], #] &] (* Michael De Vlieger, Jul 17 2016 *)

PARI

isA124273(p) = isprime(p)&&!sum(i=1, p, sum(j=0, p-1, Mod(prime(i), p)^j)) \\ Jianing Song, Oct 20 2018