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

1,2

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

Maple

G:= proc(n) local L;
    local F;
    F:= sort(ifactors(n)[2], (a, b) -> a[1]<b[1]);
    F:= map(op, subs(1=NULL, F));
    parse(cat(op(map(convert, F, string))))
end proc:
G(1):= 1:
ListTools:-PartialSums(map(G, [$1..100])); # 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 *)

Crossrefs

Cf. A080670.

Sequence in context: A074894 A324146 A363829 * A287883 A246753 A247016

Adjacent sequences: A287878 A287879 A287880 * A287882 A287883 A287884

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 19 2017

Status

approved