A343407 Number of proper divisors of n that are triangular numbers.
0, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 1, 2, 1, 1, 5, 1, 1, 2, 1, 1, 3, 1, 1, 2, 2, 1, 4, 1, 1, 3, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1, 1, 5, 1, 1, 3, 1, 1, 3, 1, 1, 2, 2, 1, 4, 1, 1, 3, 1, 1, 3, 1, 2, 2, 1, 1, 5, 1, 1, 2, 1, 1, 6, 1, 1, 2, 1, 1, 3, 1, 1, 2, 2, 1, 3, 1, 1, 4
Offset: 1
Keywords
Programs
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Maple
a:= n-> add(`if`(issqr(8*d+1), 1, 0), d=numtheory[divisors](n) minus {n}): seq(a(n), n = 1..105); # Alois P. Heinz, Apr 14 2021 -
Mathematica
nmax = 105; CoefficientList[Series[Sum[x^(k (k + 1))/(1 - x^(k (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest Table[Sum[If[d < n && IntegerQ[Sqrt[8 d + 1]], 1, 0], {d, Divisors[n]}], {n, 105}] -
PARI
a(n) = sumdiv(n, d, if ((d
Formula
G.f.: Sum_{k>=1} x^(k*(k+1)) / (1 - x^(k*(k+1)/2)).
a(n) = Sum_{d|n, d < n} A010054(d).