OFFSET
0,7
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 30 2020
STATUS
approved