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%I #17 Apr 17 2021 18:11:54
%S 2,21,124,435,1126,2447,4756,8427,13946,21865,32822,47575,66978,91787,
%T 123106,161979,209636,267195,336226,418025,514162,626453,756526,
%U 906243,1077772,1272815,1493676,1742527,2021958,2334541,2682248,3068341
%N a(n) = prime(1^3) + prime(2^3) + prime(3^3) + ... + prime(n^3).
%C Analogy with prime(1^2) + prime(2^2) + ... + prime(n^2) (A109724). If we take the cumulative sum of A055875 including the 0th value of 1, the 3rd value becomes prime(0^3) + prime(1^3) + prime(2^3) + prime(3^3) = 1 + 2 + 19 + 103 = 125 = 5^3.
%H Chai Wah Wu, <a href="/A109789/b109789.txt">Table of n, a(n) for n = 1..10000</a>
%F Cumulative sums of A055875(n) for n>0.
%e a(1) = 2 because prime(1^3) = prime(1) = 2;
%e a(2) = 21 because prime(1^3) + prime(2^3) = prime(1) + prime(8) = 2 + 19;
%e a(3) = 124 because prime(1^3) + prime(2^3) + prime(3^3) = prime(1) + prime(8) + prime(27) = 2 + 19 + 103;
%e a(4) = 435 because prime(1^3) + prime(2^3) = prime(1) + prime(8) + prime(27) + prime(64) = 2 + 19 + 103 + 311.
%e a(6) = 2 + 19 + 103 + 311 + 691 + 1321 = 2447 (which is prime).
%e a(28) = 2 + 19 + 103 + 311 + 691 + 1321 + 2309 + 3671 + 5519 + 7919 + 10957 + 14753 + 19403 + 24809 + 31319 + 38873 + 47657 + 57559 + 69031 + 81799 + 96137 + 112291 + 130073 + 149717 + 171529 + 195043 + 220861 + 248851 = 1742527 (which is prime).
%o (PARI) a(n) = sum(k=1, n, prime(k^3)); \\ _Michel Marcus_, Apr 17 2021
%Y Cf. A055875, A011757, A109724, A109770.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Aug 14 2005
%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 14 2007
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