cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A287881 Partial sums of A080670.

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%I A287881 #18 Mar 16 2020 19:02:10
%S A287881 1,3,6,28,33,56,63,86,118,143,154,377,390,417,452,476,493,725,744,969,
%T A287881 1006,1217,1240,1473,1525,1738,1771,1998,2027,2262,2293,2318,2629,
%U A287881 2846,2903,5135,5172,5391,5704,5939,5980,6217,6260,8471,8796,9019,9066,9309,9381,9633,9950,12163,12216,12449,12960
%N A287881 Partial sums of A080670.
%C A287881 It would be nice to have an estimate of how fast this sequence grows.
%C A287881 _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.
%H A287881 N. J. A. Sloane, <a href="/A287881/b287881.txt">Table of n, a(n) for n = 1..20000</a>
%H A287881 Robert Israel, <a href="/A287881/a287881.png">Graph of a(n)/(n log n)^2 for n <= 100000</a>
%p A287881 G:= proc(n) local L;
%p A287881     local F;
%p A287881     F:= sort(ifactors(n)[2],(a,b) -> a[1]<b[1]);
%p A287881     F:= map(op, subs(1=NULL,F));
%p A287881     parse(cat(op(map(convert,F,string))))
%p A287881 end proc:
%p A287881 G(1):= 1:
%p A287881 ListTools:-PartialSums(map(G, [$1..100])); # _Robert Israel_, Jun 19 2017
%t A287881 A080670 = Cases[Import["https://oeis.org/A080670/b080670.txt", "Table"], {_, _}][[All, 2]];
%t A287881 Accumulate[A080670] (* _Robert Price_, Mar 16 2020 *)
%Y A287881 Cf. A080670.
%K A287881 nonn,base
%O A287881 1,2
%A A287881 _N. J. A. Sloane_, Jun 19 2017