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%I #48 Jun 13 2021 03:22:44
%S 1,2,6,10,20,22,28,155,488,664,992,6162,7840,7975,8793,18961,32422,
%T 148220,231625,332198,459121,462932,2115894,8108930,10336641,11789731,
%U 15500046,23483195,46571611,48582404,77033887,105390951,132421841,229481560,1224959312
%N Numbers k such that k divides 1 plus the sum of the first k primes.
%C a(44) > 4.4*10^10. - _Robert Price_, Dec 15 2013
%C a(50) > 10^14. - _Bruce Garner_, Jun 05 2021
%H Bruce Garner, <a href="/A128165/b128165.txt">Table of n, a(n) for n = 1..49</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%t k = 0; s = 1; p = 2; A128165 = {}; While[k < 247336000, If[Mod[s += p, ++k] == 0, AppendTo[A128165, k]; Print[{k, p}]]; p = NextPrime@ p]; A128165
%o (PARI) is(n)=sum(i=1,n,prime(i),1)%n==0 \\ _Charles R Greathouse IV_, Nov 07 2014
%o (PARI) n=0; s=1; forprime(p=2,1e9, s+=p; if(s%n++==0, print1(n", "))) \\ _Charles R Greathouse IV_, Nov 07 2014
%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248, A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K hard,nonn
%O 1,2
%A _Alexander Adamchuk_, Feb 22 2007
%E More terms from _Ryan Propper_, Apr 05 2007
%E a(34) from _Robert G. Wilson v_, Jan 21 2011
%E a(35) from _Robert Price_, Dec 15 2013
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