A377301 - OEIS

%I #9 Oct 23 2024 08:48:54

%S 1,1,1,1,1,1,1,1,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,4,3,1,6,1,3,4,3,

%T 1,6,1,3,4,3,1,6,1,3,4,3,1,6,1,3,4,7,1,6,1,7,4,3,1,10,1,3,4,7,1,6,1,7,

%U 4,3,1,10,1,3,4,7,1,6,1,7,4,3,1,10,6,3,4,7,1,11

%N G.f.: Sum_{k>=1} k * x^(k*(4*k-3)) / (1 - x^k).

%C In general, for d > 0, if g.f. = Sum_{k>=1} k * x^(k*(d*k - d + 2)/2) / (1 - x^k), then Sum_{k=1..n} a(k) ~ 2^(3/2) * n^(3/2) / (3*sqrt(d)).

%H Vaclav Kotesovec, <a href="/A377301/b377301.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{k=1..n} a(k) ~ n^(3/2) / 3.

%t Table[Sum[If[n > 4*k*(k-1), k, 0], {k, Divisors[n]}], {n, 1, 100}]

%t nmax = 100; Rest[CoefficientList[Series[Sum[k*x^(k*(4*k - 3))/(1 - x^k), {k, 1, Sqrt[nmax/4] + 1}], {x, 0, nmax}], x]]

%Y Column 8 of A334466.

%K nonn

%O 1,10

%A _Vaclav Kotesovec_, Oct 23 2024