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.
%I A327629 #10 Jun 07 2025 18:43:21
%S A327629 1,2,4,4,5,9,7,8,12,11,11,18,13,14,21,16,17,27,19,22,29,22,23,36,25,
%T A327629 26,36,29,29,50,31,32,44,34,35,55,37,38,52,44,41,65,43,44,64,46,47,72,
%U A327629 49,55,68,52,53,81,56,58,76,58,59,100,61,62,87,64,65,100,67,68,92,77
%N A327629 Expansion of Sum_{k>=1} x^(k*(k + 1)/2) / (1 - x^(k*(k + 1)/2))^2.
%C A327629 Sum of divisors d of n such that n/d is triangular number.
%F A327629 a(n) = Sum_{d|n} A010054(n/d) * d.
%t A327629 nmax = 70; CoefficientList[Series[Sum[x^(k (k + 1)/2)/(1 - x^(k (k + 1)/2))^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A327629 a[n_] := DivisorSum[n, # &, IntegerQ[Sqrt[8 n/# + 1]] &]; Table[a[n], {n, 1, 70}]
%o A327629 (PARI) a(n)={sumdiv(n, d, if(ispolygonal(d,3), n/d))} \\ _Andrew Howroyd_, Sep 19 2019
%o A327629 (Python)
%o A327629 from sympy import divisors
%o A327629 from sympy.ntheory.primetest import is_square
%o A327629 def A327629(n): return sum(n//d for d in divisors(n,generator=True) if is_square((d<<3)+1)) # _Chai Wah Wu_, Jun 07 2025
%Y A327629 Cf. A000217, A006463, A007862, A010054, A076752, A112886 (fixed points), A185027.
%K A327629 nonn
%O A327629 1,2
%A A327629 _Ilya Gutkovskiy_, Sep 19 2019