A357311 -id:A357311 - cp's OEIS frontend

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

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Ilya Gutkovskiy, Sep 23 2022

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

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

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

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

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

cp's OEIS Frontend

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

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