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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
OFFSET
0,5
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: A064865 A178472 A337667 * A178470 A093127 A115123
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 30 2020
STATUS
approved