A263170 a(n) = (Sum_{k=1..n} prime(k))^3 - (Sum_{k=1..n} prime(k)^3).

0, 90, 840, 4410, 20118, 64890, 186168, 440730, 972030, 2094330, 4013850, 7512570, 13279548, 21906810, 34902498, 54772410, 84444690, 124785210, 181983378, 259292154, 358930146, 492406650, 664548816, 889272570, 1186319550, 1559209530, 2012668266, 2568943290, 3232452450, 4031692410

Offset: 1

Author

Altug Alkan, Oct 11 2015

Keywords

• nonn
• easy

Comments

Obviously, a(n) is always an even number.

All a(n) are divisible by 6. - Robert Israel, Oct 16 2020

Examples

			For n = 2, a(2) = (2 + 3)^3 - (2^3 + 3^3) = 90.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A098999. 3D analog of A065595.

Programs

Maple

A263170 := proc(n)
    su := add(ithprime(i),i=1..n) ;
    su3 := add(ithprime(i)^3,i=1..n) ;
    su^3-su3 ;
end proc: # R. J. Mathar, Oct 21 2015

Mathematica

Table[Sum[Prime@ k, {k, n}]^3 - Sum[Prime[k]^3, {k, n}], {n, 30}] (* Michael De Vlieger, Oct 19 2015 *)

PARI

a(n) = sum(k=1, n, prime(k))^3 - sum(k=1, n, prime(k)^3);

Formula

a(n) = A007504(n)^3 - A098999(n).

a(n) mod 2 = 0.