A287881 Partial sums of A080670.

1, 3, 6, 28, 33, 56, 63, 86, 118, 143, 154, 377, 390, 417, 452, 476, 493, 725, 744, 969, 1006, 1217, 1240, 1473, 1525, 1738, 1771, 1998, 2027, 2262, 2293, 2318, 2629, 2846, 2903, 5135, 5172, 5391, 5704, 5939, 5980, 6217, 6260, 8471, 8796, 9019, 9066, 9309, 9381, 9633, 9950, 12163, 12216, 12449, 12960

Offset: 1

Author

N. J. A. Sloane, Jun 19 2017

Keywords

• nonn
• base

Comments

It would be nice to have an estimate of how fast this sequence grows.

Robert Israel observed (see link) that for the first 100000 terms, a(n) is roughly c*n^2*(log n)^2, where c is between 0.2 and 0.25. However, the ratio a(n)/(n log n)^2 does not seem to be converging.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000
• Robert Israel, Graph of a(n)/(n log n)^2 for n <= 100000

Crossrefs

Cf. A080670.

Programs

Maple

G:= proc(n) local L;
    local F;
    F:= sort(ifactors(n)[2],(a,b) -> a[1]Robert Israel, Jun 19 2017

Mathematica

A080670 = Cases[Import["https://oeis.org/A080670/b080670.txt", "Table"], {, }][[All, 2]];
Accumulate[A080670] (* Robert Price, Mar 16 2020 *)