A234740 Sum of the eleventh powers of the first n primes.

2048, 179195, 49007320, 2026334063, 287338004674, 2079498398711, 36351394706344, 152841653604563, 1105651411518490, 13306161177224319, 38714638073629150, 216632259853089563, 766961291569338004, 1696255031040560711, 4168414246124573014, 13437450175496764611

Offset: 1

Author

Robert Price, Jan 20 2014

Keywords

• nonn
• easy

Links

• Robert Price, Table of n, a(n) for n = 1..1000
• OEIS Wiki, Sums of powers of primes divisibility sequences
• V. Shevelev, Asymptotics of sum of the first n primes with a remainder term

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

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

Partial sums of A079395.

Programs

Mathematica

Table[Sum[Prime[k]^11, {k, n}], {n, 1000}]
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 *)

PARI

s=[]; for(n=1, 15, s=concat(s, sum(i=1, n, prime(i)^11))); s \\ Colin Barker, Jan 20 2014

Formula

a(n) = Sum_{k=1..n} prime(k)^11.