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

%I A263170 #25 Oct 17 2020 02:35:46
%S A263170 0,90,840,4410,20118,64890,186168,440730,972030,2094330,4013850,
%T A263170 7512570,13279548,21906810,34902498,54772410,84444690,124785210,
%U A263170 181983378,259292154,358930146,492406650,664548816,889272570,1186319550,1559209530,2012668266,2568943290,3232452450,4031692410
%N A263170 a(n) = (Sum_{k=1..n} prime(k))^3 - (Sum_{k=1..n} prime(k)^3).
%C A263170 Obviously, a(n) is always an even number.
%C A263170 All a(n) are divisible by 6. - _Robert Israel_, Oct 16 2020
%H A263170 Robert Israel, <a href="/A263170/b263170.txt">Table of n, a(n) for n = 1..10000</a>
%F A263170 a(n) = A007504(n)^3 - A098999(n).
%F A263170 a(n) mod 2 = 0.
%e A263170 For n = 2, a(2) = (2 + 3)^3 - (2^3 + 3^3) = 90.
%p A263170 A263170 := proc(n)
%p A263170     su := add(ithprime(i),i=1..n) ;
%p A263170     su3 := add(ithprime(i)^3,i=1..n) ;
%p A263170     su^3-su3 ;
%p A263170 end proc: # _R. J. Mathar_, Oct 21 2015
%t A263170 Table[Sum[Prime@ k, {k, n}]^3 - Sum[Prime[k]^3, {k, n}], {n, 30}] (* _Michael De Vlieger_, Oct 19 2015 *)
%o A263170 (PARI) a(n) = sum(k=1, n, prime(k))^3 - sum(k=1, n, prime(k)^3);
%Y A263170 Cf. A007504, A098999. 3D analog of A065595.
%K A263170 nonn,easy
%O A263170 1,2
%A A263170 _Altug Alkan_, Oct 11 2015