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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)