OFFSET
0,7
COMMENTS
Number of ways to write n as an ordered sum of 3 perfect powers (A001597).
LINKS
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Perfect Powers
FORMULA
G.f.: (Sum_{k = i^j, i>=1, j>=2, excluding duplicates} x^k)^3.
EXAMPLE
a(14) = 6 because we have [9, 4, 1], [9, 1, 4], [4, 9, 1], [4, 1, 9], [1, 9, 4] and [1, 4, 9].
MATHEMATICA
nmax = 95; CoefficientList[Series[(x + Sum[Boole[GCD @@ FactorInteger[k][[All, 2]] > 1] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 16 2017
STATUS
approved