

A098999


Sum of cubes of the first n primes.


16



8, 35, 160, 503, 1834, 4031, 8944, 15803, 27970, 52359, 82150, 132803, 201724, 281231, 385054, 533931, 739310, 966291, 1267054, 1624965, 2013982, 2507021, 3078808, 3783777, 4696450, 5726751, 6819478, 8044521, 9339550, 10782447
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OFFSET

1,1


LINKS

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


FORMULA

a(n) = 0.25*n^4*log(n)^3 + O(n^4*log(n)^2*log(log(n))). The proof is similar to proof for A007504(n) (see link of Shevelev).  Vladimir Shevelev, Aug 02 2013


MATHEMATICA

P3[n_]:=Sum[Prime[i]^3, {i, 1, n}]; Table[P3[n], {n, 1, 60}]


PROG

(PARI) a(n) = sum(i=1, n, prime(i)^3); \\ Michel Marcus, Jan 20 2014


CROSSREFS

Partial sums of A030078.
Sequence in context: A302078 A320405 A279379 * A263520 A223901 A192257
Adjacent sequences: A098996 A098997 A098998 * A099000 A099001 A099002


KEYWORD

nonn


AUTHOR

Suzanne O' Regan (s.m.oregan(AT)student.ucc.ie), Nov 06 2004


STATUS

approved



