OFFSET
0,3
COMMENTS
Number of compositions (ordered partitions) of n into prime powers (1 included).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Prime Power
FORMULA
G.f.: 1/(1 - x - Sum_{k>=2} floor(1/omega(k))*x^k).
EXAMPLE
a(3) = 4 because we have [3], [2, 1], [1, 2] and [1, 1, 1].
MATHEMATICA
nmax = 37; CoefficientList[Series[1/(1 - x - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 05 2017
STATUS
approved