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A185027 Sum of the triangular divisors of n. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
Sequence in context: A056057 A226234 A369189 * A016520 A361731 A109955
KEYWORD
nonn
AUTHOR
Antonio Roldán, Jan 14 2013
STATUS
approved

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Last modified June 21 19:01 EDT 2024. Contains 373557 sequences. (Running on oeis4.)