A301331 Number of compositions (ordered partitions) of n into parts having the same number of divisors as n.

1, 1, 1, 1, 1, 3, 1, 6, 1, 1, 1, 20, 1, 46, 3, 1, 1, 232, 1, 501, 1, 3, 9, 2352, 1, 6, 14, 6, 1, 24442, 1, 53243, 3, 16, 55, 32, 1, 550863, 107, 55, 1, 2616338, 1, 5701553, 6, 1, 406, 27077005, 1, 25, 9, 606, 9, 280237217, 3, 1244, 1, 1839, 3185, 2900328380, 1, 6320545915, 6248, 3, 1, 7828

Offset

0,6

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to compositions

Formula

a(n) = [x^n] 1/(1 - Sum_{d(k) = d(n)} x^k).

Example

a(14) = 3 because we have [14], [8, 6] and [6, 8], where 14, 8 and 6 are numbers with 4 divisors.

Maple

with(numtheory):
a:= proc(m) option remember; local k, b; k, b:= tau(m),
      proc(n) option remember; `if`(n=0, 1,
        add(`if`(tau(j)=k, b(n-j), 0), j=1..n))
      end: b(m)
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Mar 18 2018

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[DivisorSigma[0, k] == DivisorSigma[0, n]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 65}]

Crossrefs

Cf. A000005, A300977, A300978, A301332, A301333.

Sequence in context: A337604 A117782 A317855 * A301333 A347231 A213670

Adjacent sequences: A301328 A301329 A301330 * A301332 A301333 A301334

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 18 2018

Status

approved