OFFSET
0,9
COMMENTS
Number of compositions (ordered partitions) of n into composite parts (A002808).
LINKS
Eric Weisstein's World of Mathematics, Composite Number
FORMULA
G.f.: 1/(1 - Sum_{k>=2} (1 - floor(2/d(k)))*x^k).
EXAMPLE
a(10) = 3 because we have [10], [6, 4] and [4, 6].
MATHEMATICA
nmax = 59; CoefficientList[Series[1/(1 - Sum[(1 - Floor[2/DivisorSigma[0, k]]) x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
PROG
(PARI) x='x+O('x^60); Vec(1/(1 - sum(k=2, 59, (1 - 2\numdiv(k))*x^k))) \\ Indranil Ghosh, Apr 03 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 05 2017
STATUS
approved