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A343408

Sum of proper divisors of n that are triangular numbers.

0, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 10, 1, 1, 4, 1, 1, 10, 1, 11, 4, 1, 1, 10, 1, 1, 4, 1, 1, 35, 1, 1, 4, 1, 1, 10, 1, 1, 4, 11, 1, 31, 1, 1, 19, 1, 1, 10, 1, 11, 4, 1, 1, 10, 1, 29, 4, 1, 1, 35, 1, 1, 25, 1, 1, 10, 1, 1, 4, 11, 1, 46, 1, 1, 19, 1, 1, 10, 1, 11, 4, 1, 1, 59, 1, 1, 4, 1, 1, 80, 1, 1, 4, 1, 1, 10

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..96.

FORMULA

G.f.: Sum_{k>=1} (k*(k+1)/2) * x^(k*(k+1)) / (1 - x^(k*(k+1)/2)).

a(n) = Sum_{d|n, d < n} A010054(d) * d.

MAPLE

a:= n-> add(`if`(issqr(8*d+1), d, 0), d=numtheory[divisors](n) minus {n}):

seq(a(n), n = 1..96); # Alois P. Heinz, Apr 14 2021

MATHEMATICA