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

0,5

Links

Table of n, a(n) for 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.

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}]

Crossrefs

Cf. A100346, A294137, A294138, A327642.

Sequence in context: A286254 A322664 A286457 * A147348 A081224 A104793

Adjacent sequences: A327763 A327764 A327765 * A327767 A327768 A327769

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 24 2019

Status

approved