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A232964 Numbers n such that n divides 1 + sum_{k=1,n} prime(k)^9. 0

%I

%S 1,2,4,6,10,12,14,82,93,476,712,856,935,11104,11706,12234,19500,21490,

%T 31864,171252,628863,10189718,12363588,13976077,22321041,36642393,

%U 47563206,102352700,869166585,1197804361,1400403575,2199080290,5225532140,39957170689

%N Numbers n such that n divides 1 + sum_{k=1,n} prime(k)^9.

%C a(35) > 4*10^10.

%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>

%e a(5)=10 because 1 plus the sum of the first 10 primes^9 is 16762578985600 which is divisible by 10.

%t p = 2; k = 0; s = 1; lst = {}; While[k < 40000000000, s = s + p^9; If[Mod[s, ++k] == 0, AppendTo[lst, k]; Print[{k, p}]]; p = NextPrime@ p] (* derived from A128169 *)

%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.

%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

%K nonn

%O 1,2

%A _Robert Price_, Dec 02 2013

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Last modified August 20 19:51 EDT 2019. Contains 326155 sequences. (Running on oeis4.)