A357312 Number of compositions (ordered partitions) of n into divisors of n that are smaller than sqrt(n).

1, 0, 1, 1, 1, 1, 13, 1, 34, 1, 89, 1, 927, 1, 610, 189, 1597, 1, 35890, 1, 46754, 1873, 28657, 1, 3919944, 1, 196418, 18560, 4205249, 1, 110187694, 1, 39882198, 183916, 9227465, 9496, 10312882481, 1, 63245986, 1822473, 11969319436, 1, 141930520462, 1, 34020543362, 339200673

Offset: 0

Author

Ilya Gutkovskiy, Sep 23 2022

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A100346, A294137, A294138, A327766, A357311.

Programs

Maple

a:= proc(n) option remember; uses numtheory; local b, l;
      l, b:= select(x-> is(xm, 0, b(m-j)), j=l))
      end; b(n)
    end:
seq(a(n), n=0..45);  # Alois P. Heinz, Sep 23 2022

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).