A300978 Number of partitions of n into distinct parts having the same number of divisors as n.

1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 3, 1, 2, 2, 5, 1, 1, 1, 2, 1, 7, 1, 9, 2, 3, 2, 5, 1, 11, 3, 5, 1, 14, 1, 15, 2, 1, 6, 19, 1, 1, 3, 10, 2, 26, 2, 13, 1, 15, 12, 35, 1, 39, 18, 2, 1, 22, 2, 50, 2, 27, 2, 61, 1, 67, 31, 3, 3, 39, 2, 87, 1, 1, 49, 102, 1, 55

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to partitions

Formula

a(n) = [x^n] Product_{d(k) = d(n)} (1 + x^k).

Example

a(14) = 2 because we have [14] and [8, 6], 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, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
        b(n, i-1)+`if`(tau(i)=k, b(n-i, min(i-1, n-i)), 0)))
      end: b(m$2)
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 17 2018

Mathematica

Table[SeriesCoefficient[Product[(1 + Boole[DivisorSigma[0, k] == DivisorSigma[0, n]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 85}]

Crossrefs

Cf. A000005, A300977, A300979, A300980, A300982, A300983.

Sequence in context: A358236 A330738 A025921 * A156144 A358235 A136044

Adjacent sequences: A300975 A300976 A300977 * A300979 A300980 A300981

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2018

Status

approved