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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
OFFSET
0,5
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 30 2020
STATUS
approved