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

0,7

Links

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

Formula

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

Maple

a:= proc(n) option remember; uses numtheory; local b, l;
      l, b:= select(x-> is(x<sqrt(n)), divisors(n)),
      proc(m) option remember; `if`(m=0, 1,
         add(`if`(j>m, 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}]

Crossrefs

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

Sequence in context: A123187 A272797 A046733 * A291449 A278345 A277866

Adjacent sequences: A357309 A357310 A357311 * A357313 A357314 A357315

Keyword

nonn,look

Author

Ilya Gutkovskiy, Sep 23 2022

Status

approved