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A331887 Number of partitions of n into distinct parts having a common factor > 1 with n. 3
1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 5, 1, 5, 4, 6, 1, 11, 1, 11, 6, 12, 1, 23, 3, 18, 8, 23, 1, 69, 1, 32, 13, 38, 7, 84, 1, 54, 19, 79, 1, 224, 1, 90, 46, 104, 1, 264, 5, 187, 39, 166, 1, 449, 14, 251, 55, 256, 1, 1374, 1, 340, 111, 390, 20, 1692, 1, 513, 105, 1610 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..70.

Index entries for sequences related to partitions

FORMULA

a(n) = [x^n] Product_{k: gcd(n,k) > 1} (1 + x^k).

EXAMPLE

a(12) = 5 because we have [12], [10, 2], [9, 3], [8, 4] and [6, 4, 2].

MAPLE

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

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

        `if`(igcd(i, m)>1, b(n-i, min(i-1, 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 + Boole[GCD[k, n] > 1] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 70}]

CROSSREFS

Cf. A036998, A121998, A175787 (positions of 1's), A303280, A331885, A331888.

Sequence in context: A131085 A303280 A318717 * A328220 A134192 A309342

Adjacent sequences:  A331884 A331885 A331886 * A331888 A331890 A331891

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 30 2020

STATUS

approved

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)