%I #18 Dec 23 2024 14:53:43

%S 131072,129271235,763068724360,233393582711567,505680422082005338,

%T 9156096341463343271,836396358227800107448,6316783216012602293387,

%U 147366822776675571219490,7404514559506748686057599,29954631333669491864740510,486442572159704647268887427

%N Sum of the seventeenth powers of the first n primes.

%H Robert Price, <a href="/A236225/b236225.txt">Table of n, a(n) for n = 1..1000</a>

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

%H Vladimir Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-August/011512.html">Asymptotics of sum of the first n primes with a remainder term</a>

%F a(n) = Sum_{k=1..n} prime(k)^17.

%t Table[Sum[Prime[k]^17, {k, n}], {n, 1000}]

%t Accumulate[Prime[Range[20]]^17] (* _Harvey P. Dale_, Nov 05 2016 *)

%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.

%Y Partial sums of A138032.

%K nonn,easy

%O 1,1

%A _Robert Price_, Jan 20 2014