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 A343407 Number of proper divisors of n that are triangular numbers. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Table of n, a(n) for n=1..105. 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). 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}] PROG (PARI) a(n) = sumdiv(n, d, if ((d

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Last modified September 23 19:57 EDT 2023. Contains 365554 sequences. (Running on oeis4.)