OFFSET
0,5
COMMENTS
Number of compositions (ordered partitions) into prime powers (1 excluded).
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 - Sum_{k>=2} floor(1/omega(k))*x^k).
EXAMPLE
a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].
MATHEMATICA
nmax = 48; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 28 2016
STATUS
approved