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%I #23 Sep 17 2023 16:13:38
%S 2048,179195,49007320,2026334063,287338004674,2079498398711,
%T 36351394706344,152841653604563,1105651411518490,13306161177224319,
%U 38714638073629150,216632259853089563,766961291569338004,1696255031040560711,4168414246124573014,13437450175496764611
%N Sum of the eleventh powers of the first n primes.
%H Robert Price, <a href="/A234740/b234740.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 V. 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)^11.
%t Table[Sum[Prime[k]^11, {k, n}], {n, 1000}]
%t Accumulate[Prime[Range[20]]^11] (* This program is several hundred times faster than the first program, above, in calculating the first 1000 terms of the sequence. *) (* _Harvey P. Dale_, Sep 17 2023 *)
%o (PARI) s=[]; for(n=1, 15, s=concat(s, sum(i=1, n, prime(i)^11))); s \\ _Colin Barker_, Jan 20 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.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%Y Partial sums of A079395.
%K nonn,easy
%O 1,1
%A _Robert Price_, Jan 20 2014
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