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