OFFSET
0,4
COMMENTS
Number of ways to write n as an ordered sum of two prime powers (1 included).
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
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))^2.
EXAMPLE
a(8) = 5 because we have [7, 1], [5, 3], [4, 4], [3, 5] and [1, 7].
MAPLE
N:= 100: # to get a(0)..a(N)
P:= select(isprime, [$2..N]):
g:= x + add(add(x^(p^k), k=1..floor(log[p](N))), p=P):
S:= series(g^2, x, N+1):
seq(coeff(S, x, n), n=0..N); # Robert Israel, Feb 10 2017
MATHEMATICA
nmax = 95; CoefficientList[Series[(x + Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Feb 05 2017
STATUS
approved