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A331888 Number of compositions (ordered partitions) of n into parts having a common factor > 1 with n. 5
1, 0, 1, 1, 2, 1, 5, 1, 8, 4, 17, 1, 60, 1, 65, 19, 128, 1, 800, 1, 683, 67, 1025, 1, 11005, 16, 4097, 256, 9203, 1, 369426, 1, 32768, 1027, 65537, 79, 2124475, 1, 262145, 4099, 1424118, 1, 48987720, 1, 2127107, 96334, 4194305, 1, 411836297, 64, 67919981, 65539 (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 compositions

FORMULA

a(n) = [x^n] 1 / (1 - Sum_{k: gcd(n,k) > 1} x^k).

EXAMPLE

a(9) = 4 because we have [9], [6, 3], [3, 6] and [3, 3, 3].

MAPLE

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

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

        add(`if`(igcd(j, m)>1, b(n-j), 0), j=1..n))

      end; forget(b); b(m$2)

    end:

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

MATHEMATICA

Table[SeriesCoefficient[1/(1 - Sum[Boole[GCD[k, n] > 1] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 51}]

CROSSREFS

Cf. A182986 (positions of 1's), A100347, A121998, A178472, A331885, A331887.

Sequence in context: A124227 A064865 A178472 * A178470 A093127 A115123

Adjacent sequences:  A331885 A331886 A331887 * A331890 A331891 A331892

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.)