OFFSET
0,28
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Composite Number
FORMULA
G.f.: ((1 - x)/(1 - x^2))*Product_{k>=1} (1 - x^(2*k))*(1 - x^prime(k))/(1 - x^k).
EXAMPLE
a(36) = 3 because we have [27, 9], [21, 15] and [9, 9, 9, 9].
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(add(
`if`(d>1 and d::odd and not isprime(d), d, 0),
d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..100); # Alois P. Heinz, Dec 31 2016
MATHEMATICA
nmax = 100; CoefficientList[Series[(1 - x)/(1 - x^2) Product[(1 - x^(2 k)) (1 - x^Prime[k])/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 31 2016
STATUS
approved