

A282499


Expansion of (Sum_{k = i^j, i>=1, j>=2, excluding duplicates} x^k)^3.


1



0, 0, 0, 1, 0, 0, 3, 0, 0, 3, 3, 3, 1, 6, 6, 0, 3, 6, 9, 3, 3, 12, 3, 0, 4, 9, 9, 4, 6, 9, 6, 0, 9, 12, 12, 9, 9, 18, 9, 6, 12, 18, 18, 6, 21, 21, 6, 6, 10, 24, 9, 12, 15, 18, 12, 3, 18, 12, 18, 12, 18, 24, 15, 9, 9, 18, 24, 15, 18, 24, 9, 6, 18, 24, 12, 13, 15, 27, 6, 9, 15, 19, 18, 9, 24, 12, 18, 0, 15, 24, 27, 9, 12, 24, 12, 12
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OFFSET

0,7


COMMENTS

Number of ways to write n as an ordered sum of 3 perfect powers (A001597).


LINKS

Table of n, a(n) for n=0..95.
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

Cf. A001597, A078635, A113505.
Sequence in context: A178952 A178153 A267794 * A216194 A279168 A111787
Adjacent sequences: A282496 A282497 A282498 * A282500 A282501 A282502


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Feb 16 2017


STATUS

approved



