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A331885 Number of partitions of n into parts having a common factor > 1 with n. 4
1, 0, 1, 1, 2, 1, 4, 1, 5, 3, 8, 1, 16, 1, 16, 9, 22, 1, 51, 1, 51, 17, 57, 1, 147, 7, 102, 30, 152, 1, 620, 1, 231, 58, 298, 21, 946, 1, 491, 103, 921, 1, 3249, 1, 1060, 325, 1256, 1, 4866, 15, 3157, 299, 2539, 1, 10369, 62, 4846, 492, 4566, 1, 45786, 1, 6843 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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_{k: gcd(n,k) > 1} 1 / (1 - x^k).

EXAMPLE

a(6) = 4 because we have [6], [4, 2], [3, 3] and [2, 2, 2].

MAPLE

a:= proc(m) option remember; local b; b:=

      proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0,

       `if`(igcd(i, m)>1, b(n-i, min(i, n-i)), 0)+b(n, i-1)))

      end; forget(b); b(m$2)

    end:

seq(a(n), n=0..82);  # Alois P. Heinz, Jan 30 2020

MATHEMATICA

Table[SeriesCoefficient[Product[1/(1 - Boole[GCD[k, n] > 1] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 62}]

CROSSREFS

Cf. A182986 (positions of 1's), A018783, A057562, A121998, A331887, A331888.

Sequence in context: A018783 A200976 A328187 * A298971 A328602 A218970

Adjacent sequences:  A331882 A331883 A331884 * A331886 A331887 A331888

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 30 2020

STATUS

approved

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Last modified June 13 06:07 EDT 2021. Contains 344981 sequences. (Running on oeis4.)