OFFSET
0,5
COMMENTS
Number of ways to write n as an ordered sum of three prime powers (1 included).
LINKS
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Prime Power
FORMULA
G.f.: (x + Sum_{p prime, k>=1} x^(p^k))^3.
EXAMPLE
a(6) = 10 because we have [4, 1, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 2, 2], [2, 1, 3], [1, 4, 1], [1, 3, 2], [1, 2, 3] and [1, 1, 4].
MATHEMATICA
nmax = 70; CoefficientList[Series[(x + Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 05 2017
STATUS
approved