A236182 Sum of the sixth powers of the first n primes.

64, 793, 16418, 134067, 1905628, 6732437, 30870006, 77915887, 225951776, 820775097, 1708278778, 4274005187, 9024109428, 15345472477, 26124687806, 48289048935, 90469582576, 141989956937, 232448339106, 360548623027, 511882849316, 754970304837, 1081910678206

Offset: 1

Author

Robert Price, Jan 19 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
• Vladimir Shevelev, Asymptotics of sum of the first n primes with a remainder term, SeqFan Mailing List, Aug 01 2013.

Crossrefs

Cf. A030516 (6th powers of primes).

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.

Programs

Mathematica

Table[Sum[Prime[k]^6, {k, n}], {n, 100}]
Accumulate[Prime[Range[30]]^6] (* Harvey P. Dale, Oct 29 2023 *)

PARI

a(n) = sum(k=1, n, prime(k)^6); \\ Michel Marcus, Mar 01 2022

Formula

a(n) = Sum_{k = 1..n} prime(k)^6.