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A300977 Number of partitions of n into parts having the same number of divisors as n. 7
1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 6, 1, 9, 2, 1, 1, 17, 1, 23, 1, 2, 4, 40, 1, 2, 5, 3, 1, 87, 1, 111, 2, 5, 10, 7, 1, 219, 14, 9, 1, 336, 1, 413, 3, 1, 26, 614, 1, 4, 3, 30, 4, 1083, 2, 42, 1, 51, 66, 1850, 1, 2198, 91, 2, 1, 95, 2, 3630, 9, 130, 2, 5007, 1, 5861, 209, 3, 11, 232, 3, 9282, 1 (list; graph; refs; listen; history; text; internal format)
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/(1 - x^k).

EXAMPLE

a(27) = 3 because we have [27], [21, 6] and [15, 6, 6], where 27, 21, 15 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`(n=0, 1, `if`(i<1, 0,

        b(n, i-1)+`if`(tau(i)=k, b(n-i, min(i, 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/(1 - Boole[DivisorSigma[0, k] == DivisorSigma[0, n]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 80}]

CROSSREFS

Cf. A000005, A300978, A300979, A300980, A300982, A300983.

Sequence in context: A057021 A152443 A119804 * A144869 A247564 A193870

Adjacent sequences:  A300974 A300975 A300976 * A300978 A300979 A300980

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 17 2018

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)