OFFSET
1,1
COMMENTS
a(45) > 491952295618219. - Bruce Garner, Jun 02 2021
LINKS
Bruce Garner, Table of n, a(n) for n = 1..44 (first 37 terms from Robert Price, terms 38..39 from Karl-Heinz Hofmann)
EXAMPLE
13 is a term because 13 is the 6th prime and the sum of the first 6 primes^17+1 = 9156096341463343272 when divided by 6 equals 1526016056910557212 which is an integer.
MATHEMATICA
t = {}; sm = 1; Do[sm = sm + Prime[n]^17; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
With[{nn=175*10^8}, Prime[#]&/@Select[Thread[{Range[nn], Accumulate[ Prime[ Range[nn]]^17]}], Divisible[#[[2]]+1, #[[1]]]&][[All, 1]]] (* The program will take a long time to run *) (* Harvey P. Dale, Apr 13 2018 *)
PROG
(PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^17); s==0 \\ Charles R Greathouse IV, Nov 30 2013
CROSSREFS
Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
KEYWORD
nonn
AUTHOR
Robert Price, Dec 12 2013
STATUS
approved