cp's OEIS Frontend

A334987 Sum of centered triangular numbers dividing n.

%I A334987 #12 Feb 16 2025 08:34:00
%S A334987 1,1,1,5,1,1,1,5,1,11,1,5,1,1,1,5,1,1,20,15,1,1,1,5,1,1,1,5,1,11,32,5,
%T A334987 1,1,1,5,1,20,1,15,1,1,1,5,1,47,1,5,1,11,1,5,1,1,1,5,20,1,1,15,1,32,1,
%U A334987 69,1,1,1,5,1,11,1,5,1,1,1,24,1,1,1,15,1,1,1,5,86,1,1,5,1,11
%N A334987 Sum of centered triangular numbers dividing n.
%H A334987 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%F A334987 G.f.: Sum_{k>=1} (3*k*(k - 1)/2 + 1) * x^(3*k*(k - 1)/2 + 1) / (1 - x^(3*k*(k - 1)/2 + 1)).
%F A334987 L.g.f.: log(G(x)), where G(x) is the g.f. for A280950.
%t A334987 nmax = 90; CoefficientList[Series[Sum[(3 k (k - 1)/2 + 1) x^(3 k (k - 1)/2 + 1)/(1 - x^(3 k (k - 1)/2 + 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A334987 nmax = 90; CoefficientList[Series[Log[Product[1/(1 - x^(3 k (k - 1)/2 + 1)), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest
%o A334987 (PARI) isc(n) = my(k=(2*n-2)/3, m); (n==1) || ((denominator(k)==1) && (m=sqrtint(k)) && (m*(m+1)==k));
%o A334987 a(n) = sumdiv(n, d, if (isc(d), d)); \\ _Michel Marcus_, May 19 2020
%Y A334987 Cf. A005448, A185027, A280950, A300409, A334988.
%K A334987 nonn
%O A334987 1,4
%A A334987 _Ilya Gutkovskiy_, May 18 2020