A065595 -id:A065595 - cp's OEIS frontend

A065762 a(n) = (sum of first n primes)^2 + sum of (squares of first n primes).

8, 38, 138, 376, 992, 2058, 4030, 6956, 11556, 19038, 28958, 43536, 63052, 87218, 118050, 158436, 210356, 271478, 347590, 438328, 542280, 667258, 812342, 983756, 1189396, 1423918, 1684302, 1977696, 2300336, 2660354, 3097234, 3582196, 4126908, 4718214

Offset: 1

Terrel Trotter, Jr., Dec 04 2001

			a(4) = 376 because (2 + 3 + 5 + 7)^2 + (2^2 + 3^2 + 5^2 + 7^2) = 17^2 + (4 + 9 + 25 + 49) = 289 + 87 = 376.

Harry J. Smith, Table of n, a(n) for n = 1..500

Cf. A007504, A024450, A065595.

nn=50;With[{prs=Prime[Range[nn]]},Table[Total[Take[prs,n]]^2+ Total[Take[prs,n]^2],{n,nn}]] (* Harvey P. Dale, Aug 20 2011 *)

{ s=ss=0; for (n=1, 500, p=prime(n); s+=p; ss+=p^2; write("b065762.txt", n, " ", s^2 + ss) ) } \\ Harry J. Smith, Oct 30 2009

a(n) = A007504(n)^2 + A024450(n). - Michel Marcus, Oct 12 2015

More terms from Harvey P. Dale, Aug 20 2011

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

Original entry on oeis.org

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

Altug Alkan, Oct 11 2015

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

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

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

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

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

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

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

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

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

a(n) mod 2 = 0.

cp's OEIS Frontend

A065762 a(n) = (sum of first n primes)^2 + sum of (squares of first n primes).

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