A185027 Sum of the triangular divisors of n.

1, 1, 4, 1, 1, 10, 1, 1, 4, 11, 1, 10, 1, 1, 19, 1, 1, 10, 1, 11, 25, 1, 1, 10, 1, 1, 4, 29, 1, 35, 1, 1, 4, 1, 1, 46, 1, 1, 4, 11, 1, 31, 1, 1, 64, 1, 1, 10, 1, 11, 4, 1, 1, 10, 56, 29, 4, 1, 1, 35, 1, 1, 25, 1, 1, 76, 1, 1, 4, 11, 1, 46, 1, 1, 19, 1, 1, 88, 1

Offset

1,3

Links

Antonio Roldán, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^(k*(k+1)/2)/(1 - x^(k*(k+1)/2)). - Ilya Gutkovskiy, Dec 24 2016

Example

a(15) = 19 because 1+3+15 = 19 (1, 3 and 15 are the triangular divisors of 15).

Mathematica

a[n_] := DivisorSum[n, # &, IntegerQ[Sqrt[8*#+1]] &]; Array[a, 100] (* Amiram Eldar, Aug 12 2023 *)

Prog

(PARI)
istriang(x)=issquare(8*x+1)
sumdivtriang(n)=m=0; for(i=1, n, if(istriang(i)&&n/i==n\i, m+=i)); return(m)}
{for(n=1, 10^4, k=sumdivtriang(n); write("b185027.txt", n, " ", k))}
(PARI) a(n)=sumdiv(n, d, ispolygonal(d, 3)*d) \\ Charles R Greathouse IV, Jan 14 2013

Crossrefs

Cf. A000217, A035316.

Sequence in context: A056057 A226234 A369189 * A016520 A361731 A109955

Adjacent sequences: A185024 A185025 A185026 * A185028 A185029 A185030

Keyword

nonn

Author

Antonio Roldán, Jan 14 2013

Status

approved