A282500 - OEIS

%I #6 Feb 17 2017 09:53:12

%S 1,1,1,1,2,3,4,5,8,13,19,26,37,55,81,116,167,244,358,520,752,1091,

%T 1589,2311,3354,4870,7081,10298,14963,21734,31580,45900,66704,96919,

%U 140827,204654,297413,432180,627996,912565,1326117,1927054,2800260,4069160,5913116,8592675,12486402,18144506,26366614

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

%C Number of compositions (ordered partitions) into perfect powers (A001597).

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

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

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

%F a(n) ~ c / r^n, where r = 0.68816189979082638501485812136220175833447947220530020978433949588627... and c = 0.4267808681995359684192168334905096310027880655306734537865362460298... . - _Vaclav Kotesovec_, Feb 17 2017

%e a(7) = 5 because we have  [4, 1, 1, 1], [1, 4, 1, 1], [1, 1, 4, 1], [1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1].

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

%Y Cf. A001597, A078635, A112344.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Feb 16 2017