A109789 a(n) = prime(1^3) + prime(2^3) + prime(3^3) + ... + prime(n^3).

2, 21, 124, 435, 1126, 2447, 4756, 8427, 13946, 21865, 32822, 47575, 66978, 91787, 123106, 161979, 209636, 267195, 336226, 418025, 514162, 626453, 756526, 906243, 1077772, 1272815, 1493676, 1742527, 2021958, 2334541, 2682248, 3068341

Offset

1,1

Comments

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

Cumulative sums of A055875(n) for n>0.

Example

a(1) = 2 because prime(1^3) = prime(1) = 2;
a(2) = 21 because prime(1^3) + prime(2^3) = prime(1) + prime(8) = 2 + 19;
a(3) = 124 because prime(1^3) + prime(2^3) + prime(3^3) = prime(1) + prime(8) + prime(27) = 2 + 19 + 103;
a(4) = 435 because prime(1^3) + prime(2^3) = prime(1) + prime(8) + prime(27) + prime(64) = 2 + 19 + 103 + 311.
a(6) = 2 + 19 + 103 + 311 + 691 + 1321 = 2447 (which is prime).
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).

Prog

(PARI) a(n) = sum(k=1, n, prime(k^3)); \\ Michel Marcus, Apr 17 2021

Crossrefs

Cf. A055875, A011757, A109724, A109770.

Sequence in context: A188530 A178328 A091789 * A136588 A171009 A098661

Adjacent sequences: A109786 A109787 A109788 * A109790 A109791 A109792

Keyword

nonn

Author

Jonathan Vos Post, Aug 14 2005

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 14 2007

Status

approved