A236215 - OEIS

%I #16 Jan 02 2023 12:30:50

%S 512,20195,1973320,42326927,2400274618,13004773991,131592650488,

%T 454280348267,2255433009730,16762578985599,43202201146270,

%U 173163940941347,500545875335308,1003138487272151,2122268960374918,5422032552177051,14085028370831990,25779174463666131

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

%H Robert Price, <a href="/A236215/b236215.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="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)^9.

%t Table[Sum[Prime[k]^9, {k, n}], {n, 1000}]

%t Accumulate[Prime[Range[20]]^9] (* _Harvey P. Dale_, Jul 01 2015 *)

%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 A179665.

%K nonn,easy

%O 1,1

%A _Robert Price_, Jan 20 2014