A109724 Sum of the first n^2 primes.

0, 2, 17, 100, 381, 1060, 2427, 4888, 8893, 15116, 24133, 36888, 54169, 77136, 106733, 144526, 191755, 249748, 320705, 406048, 507825, 627294, 768373, 931686, 1119887, 1336090, 1583293, 1864190, 2180741, 2536646, 2935471, 3380980

Offset: 0

Author

Giovanni Teofilatto, Aug 10 2005

Keywords

• easy
• nonn

Comments

Partial sums of A109725.

a(n) = A007504(n^2).

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

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

Links

• Ray Chandler, Table of n, a(n) for n = 0..10000 (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]

Crossrefs

Cf. A007504, A109722-A109726, A122207, A122208.

Programs

Mathematica

f[n_] := Sum[Prime[k], {k, n}]; Table[f[n^2], {n, 0, 32}]

PARI

a(n)=vecsum(primes(n^2)) \\ Charles R Greathouse IV, Sep 15 2015

Formula

a(n) ~ n^4 log n. - Charles R Greathouse IV, Sep 15 2015 (Corrected by N. J. A. Sloane, Jan 19 2019)

Extensions

Edited and extended by Ray Chandler, Aug 11 2005