OFFSET
0,9
COMMENTS
Number of compositions (ordered partitions) of n into proper prime powers (A246547).
LINKS
Eric Weisstein's World of Mathematics, Prime Power
FORMULA
G.f.: 1/(1 - Sum_{p prime, k>=2} x^(p^k)).
EXAMPLE
a(12) = 3 because we have [8, 4], [4, 8] and [4, 4, 4].
MATHEMATICA
nmax = 67; CoefficientList[Series[1/(1 - Sum[Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
PROG
(PARI) x='x+O('x^68); Vec(1/(1 - sum(k=2, 67, sign(bigomega(k) - 1) * (1\omega(k)) * x^k))) \\ Indranil Ghosh, Apr 03 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 06 2017
STATUS
approved