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A109724 Sum of the first n^2 primes.

%I A109724 #23 Jan 19 2019 12:29:11
%S A109724 0,2,17,100,381,1060,2427,4888,8893,15116,24133,36888,54169,77136,
%T A109724 106733,144526,191755,249748,320705,406048,507825,627294,768373,
%U A109724 931686,1119887,1336090,1583293,1864190,2180741,2536646,2935471,3380980
%N A109724 Sum of the first n^2 primes.
%C A109724 Partial sums of A109725.
%C A109724 a(n) = A007504(n^2).
%C A109724 a(n) = A109724(n) is prime for a(1) = 2, a(2) = 17, a(8) = 8893, a(10) = 24133, a(22) = 68373, a(26) = 1583293, a(28) = 2180741. a(n) is semiprime for a(4) = 381 = 3 * 127, a(6) = 2427 = 3 * 809, a(12) = 54169 = 19 * 2851, a(16) = 191755 = 5 * 38351, a(24) = 1119887 = 89 * 12583. a(n) is square for a(3) = 100. These subsequences might be worth extending. - _Jonathan Vos Post_, Aug 13 2005
%C A109724 Prime a(n) are listed in A122207[n] = {2,17,8893,24133,768373,1583293,2180741,3875933,6426919,173472547,289093219,741938801,2738357903,2895147163,3058653607,...}. Numbers n such that a(n) is a prime are listed in A122208[n] = {1,2,8,10,22,26,28,32,36,78,88,110,150,152,154,...}. - _Alexander Adamchuk_, Aug 25 2006
%H A109724 Ray Chandler, <a href="/A109724/b109724.txt">Table of n, a(n) for n = 0..10000</a> (first 500 terms from Vincenzo Librandi) [It was suggested that the initial terms of this b-file were wrong, but in fact they are correct. - _N. J. A. Sloane_, Jan 19 2019]
%F A109724 a(n) ~ n^4 log n. - _Charles R Greathouse IV_, Sep 15 2015 (Corrected by _N. J. A. Sloane_, Jan 19 2019)
%t A109724 f[n_] := Sum[Prime[k], {k, n}]; Table[f[n^2], {n, 0, 32}]
%o A109724 (PARI) a(n)=vecsum(primes(n^2)) \\ _Charles R Greathouse IV_, Sep 15 2015
%Y A109724 Cf. A007504, A109722-A109726, A122207, A122208.
%K A109724 easy,nonn
%O A109724 0,2
%A A109724 _Giovanni Teofilatto_, Aug 10 2005
%E A109724 Edited and extended by _Ray Chandler_, Aug 11 2005