A327766 Number of compositions (ordered partitions) of n into divisors of n that are at most sqrt(n).

1, 1, 1, 1, 5, 1, 13, 1, 34, 19, 89, 1, 927, 1, 610, 189, 4930, 1, 35890, 1, 46754, 1873, 28657, 1, 3919944, 571, 196418, 18560, 4205249, 1, 110187694, 1, 39882198, 183916, 9227465, 9496, 14484956252, 1, 63245986, 1822473, 11969319436, 1, 141930520462, 1, 34020543362, 339200673

Offset: 0

Author

Ilya Gutkovskiy, Sep 24 2019

Keywords

• nonn

Crossrefs

Cf. A100346, A294137, A294138, A327642.

Programs

Mathematica

a[n_] := SeriesCoefficient[1/(1 - Sum[Boole[d <= Sqrt[n]] x^d, {d, Divisors[n]}]), {x, 0, n}]; Table[a[n], {n, 0, 45}]

Formula

a(n) = [x^n] 1 / (1 - Sum_{d|n, d <= sqrt(n)} x^d).

a(p) = 1, where p is prime.