|
%I #18 Jan 02 2023 12:30:46
%S 8,35,160,503,1834,4031,8944,15803,27970,52359,82150,132803,201724,
%T 281231,385054,533931,739310,966291,1267054,1624965,2013982,2507021,
%U 3078808,3783777,4696450,5726751,6819478,8044521,9339550,10782447
%N Sum of cubes of the first n primes.
%H Robert Price, <a href="/A098999/b098999.txt">Table of n, a(n) for n = 1..1000</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>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%F 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
%t P3[n_]:=Sum[Prime[i]^3, {i, 1, n}];Table[P3[n], {n, 1, 60}]
%o (PARI) a(n) = sum(i=1, n, prime(i)^3); \\ _Michel Marcus_, Jan 20 2014
%Y Partial sums of A030078.
%K nonn
%O 1,1
%A Suzanne O' Regan (s.m.oregan(AT)student.ucc.ie), Nov 06 2004
|
