OFFSET
0,7
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..10000 (computed from the b-file of A211110 provided by Alois P. Heinz)
FORMULA
a(n) = [x^n] Product_{d|n, 1 < d < n} 1/(1 - x^d).
a(n) = A211110(n) - 1 for n > 1.
EXAMPLE
a(6) = 2 because 6 has 4 divisors {1, 2, 3, 6} among which 2 are nontrivial divisors {2, 3} therefore we have [3, 3] and [2, 2, 2].
MAPLE
with(numtheory):
a:= proc(n) local b, l; l:= sort([(divisors(n) minus {1, n})[]]):
b:= proc(m, i) option remember; `if`(m=0, 1, `if`(i<1, 0,
b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i))))
end; forget(b):
b(n, nops(l))
end:
seq(a(n), n=0..100); # Alois P. Heinz, Oct 16 2017
MATHEMATICA
Table[d = Divisors[n]; Coefficient[Series[Product[1/(1 - Boole[d[[k]] != 1 && d[[k]] != n] x^d[[k]]), {k, Length[d]}], {x, 0, n}], x, n], {n, 0, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 16 2017
STATUS
approved