OFFSET
0,21
COMMENTS
Number of ways to write n as an ordered sum of 4 proper prime powers (A246547).
Conjecture: a(n) > 0 for all n > 27.
LINKS
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Prime Power
FORMULA
G.f.: (Sum_{p prime, k>=2} x^(p^k))^4.
EXAMPLE
a(28) = 8 because we have [16, 4, 4, 4], [8, 8, 8, 4], [8, 8, 4, 8], [8, 4, 8, 8], [4, 16, 4, 4], [4, 8, 8, 8], [4, 4, 16, 4] and [4, 4, 4, 16].
MATHEMATICA
nmax = 91; CoefficientList[Series[Sum[Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]^4, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 11 2017
STATUS
approved