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

Author

Antonio Roldán, Jan 14 2013

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A000217, A035316.

Programs

Mathematica

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

PARI

istriang(x)=issquare(8*x+1)
a(n)={my(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

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