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a(n) = (sum of first n primes)^2 - sum of squares of first n primes.
3

%I #15 Oct 12 2015 01:50:12

%S 0,12,62,202,576,1304,2698,4902,8444,14244,22242,34082,50236,70704,

%T 97118,131886,176844,230524,297658,378314,471608,584104,715410,870982,

%U 1057804,1271924,1511090,1781586,2080464,2414944,2819566,3270206

%N a(n) = (sum of first n primes)^2 - sum of squares of first n primes.

%H Harry J. Smith, <a href="/A065595/b065595.txt">Table of n, a(n) for n=1,...,500</a>

%F a(n) = (A007504(n))^2 - A024450(n). - _R. J. Mathar_, Oct 07 2011

%e a(4) = 202 because (2 + 3 + 5 + 7)^2 - (2^2 + 3^2 + 5^2 + 7^2) = 17^2 - (4 + 9 + 25 + 49) = 289 - 87 = 202

%t With[{prs=Prime[Range[40]]},Table[Total[Take[prs,n]]^2-Total[Take[ prs,n]^2], {n,40}]] (* _Harvey P. Dale_, Dec 04 2011 *)

%o (PARI) { a1=a2=0; for (n=1, 500, a1+=prime(n); a2+=prime(n)^2; write("b065595.txt", n, " ", a1^2 - a2) ) } \\ _Harry J. Smith_, Oct 23 2009

%Y Cf. A007504, A024450.

%K easy,nonn

%O 1,2

%A _Terrel Trotter, Jr._, Dec 01 2001

%E a(26)-a(32) from _Harry J. Smith_, Oct 23 2009