A377300 - OEIS

%I #10 Oct 23 2024 08:47:53

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

%T 3,4,3,1,6,1,3,4,3,1,6,5,3,4,3,5,6,1,3,8,3,1,6,5,3,4,3,5,6,1,3,8,3,1,

%U 6,5,3,4,3,5,11,1,3,8,3,6,6,5,3,4,8,5,6,1,3,13

%N G.f.: Sum_{k>=1} k * x^(k*(7*k - 7 + 2)/2) / (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="/A377300/b377300.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{k=1..n} a(k) ~ 2^(3/2) * n^(3/2) / (3*sqrt(7)).

%t Table[Sum[If[n > 7*k*(k-1)/2 && IntegerQ[n/k - 7*(k-1)/2], k, 0], {k, Divisors[2*n]}], {n, 1, 100}]

%t nmax = 100; Rest[CoefficientList[Series[Sum[k*x^(k*(7*k - 7 + 2)/2)/(1 - x^k), {k, 1, Sqrt[2*nmax/7] + 1}], {x, 0, nmax}], x]]

%Y Column 7 of A334466.

%K nonn

%O 1,9

%A _Vaclav Kotesovec_, Oct 23 2024