A098999 Sum of cubes of the first n primes.

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

Offset: 1

Author

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

Keywords

• nonn

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

Crossrefs

Partial sums of A030078.

Programs

Mathematica

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

PARI

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

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