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A300978 Number of partitions of n into distinct parts having the same number of divisors as n. 7
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 (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 + 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: A316190 A330738 A025921 * A156144 A136044 A184240

Adjacent sequences:  A300975 A300976 A300977 * A300979 A300980 A300981

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 17 2018

STATUS

approved

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Last modified December 5 09:47 EST 2020. Contains 338945 sequences. (Running on oeis4.)