

A185027


Sum of the triangular divisors of n.


6



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
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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 triangular divisors of 15).


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. A035316.
Sequence in context: A056647 A056057 A226234 * A016520 A109955 A214398
Adjacent sequences: A185024 A185025 A185026 * A185028 A185029 A185030


KEYWORD

nonn


AUTHOR

Antonio Roldán, Jan 14 2013


STATUS

approved



