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A282499 Expansion of (Sum_{k = i^j, i>=1, j>=2, excluding duplicates} x^k)^3. 1

%I #9 Mar 28 2017 14:57:50

%S 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,

%T 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,

%U 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

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

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

%H Ilya Gutkovskiy, <a href="/A282499/a282499.pdf">Extended graphical example</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Powers</a>

%F G.f.: (Sum_{k = i^j, i>=1, j>=2, excluding duplicates} x^k)^3.

%e 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].

%t nmax = 95; CoefficientList[Series[(x + Sum[Boole[GCD @@ FactorInteger[k][[All, 2]] > 1] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]

%Y Cf. A001597, A078635, A113505.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Feb 16 2017

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)