cp's OEIS Frontend

A343408 Sum of proper divisors of n that are triangular numbers.

%I A343408 #8 Apr 14 2021 09:20:47
%S A343408 0,1,1,1,1,4,1,1,4,1,1,10,1,1,4,1,1,10,1,11,4,1,1,10,1,1,4,1,1,35,1,1,
%T A343408 4,1,1,10,1,1,4,11,1,31,1,1,19,1,1,10,1,11,4,1,1,10,1,29,4,1,1,35,1,1,
%U A343408 25,1,1,10,1,1,4,11,1,46,1,1,19,1,1,10,1,11,4,1,1,59,1,1,4,1,1,80,1,1,4,1,1,10
%N A343408 Sum of proper divisors of n that are triangular numbers.
%F A343408 G.f.: Sum_{k>=1} (k*(k+1)/2) * x^(k*(k+1)) / (1 - x^(k*(k+1)/2)).
%F A343408 a(n) = Sum_{d|n, d < n} A010054(d) * d.
%p A343408 a:= n-> add(`if`(issqr(8*d+1), d, 0), d=numtheory[divisors](n) minus {n}):
%p A343408 seq(a(n), n = 1..96);  # _Alois P. Heinz_, Apr 14 2021
%t A343408 nmax = 96; CoefficientList[Series[Sum[(k (k + 1)/2) x^(k (k + 1))/(1 - x^(k (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A343408 Table[Sum[If[d < n && IntegerQ[Sqrt[8 d + 1]], d, 0], {d, Divisors[n]}], {n, 96}]
%o A343408 (PARI) a(n) = sumdiv(n, d, if ((d<n) && ispolygonal(d, 3), d)); \\ _Michel Marcus_, Apr 14 2021
%Y A343408 Cf. A000217, A001065, A010054, A185027, A293235, A343407.
%K A343408 nonn
%O A343408 1,6
%A A343408 _Ilya Gutkovskiy_, Apr 14 2021