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Number of compositions (ordered partitions) of n into cubes dividing n.
0

%I #10 Oct 30 2017 03:54:36

%S 1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,64,1,1,2,1,1,1,1,

%T 345,1,1,1,1,1,1,1,1824,1,1,1,1,1,1,1,9661,1,1,1,1,1,30,1,51284,1,1,1,

%U 1,1,1,1,272334,1,1,1,1,1,1,1,1445995,1,1,1,1,1,1,1,7677250,463,1,1,1,1

%N Number of compositions (ordered partitions) of n into cubes dividing n.

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

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%F a(m)=1 when m is cubefree (A004709) and a(m)<>1 when m is not cubefree (A046099). - _Michel Marcus_, Oct 29 2017

%e a(16) = 11 because 16 has 5 divisors {1, 2, 4, 8, 16} among which 2 are cubes {1, 8} therefore we have [8, 8], [8, 1, 1, 1, 1, 1, 1, 1, 1], [1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 1, 1, 1, 1, 1, 1], [1, 1, 1, 8, 1, 1, 1, 1, 1], [1, 1, 1, 1, 8, 1, 1, 1, 1], [1, 1, 1, 1, 1, 8, 1, 1, 1], [1, 1, 1, 1, 1, 1, 8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 8, 1], [1, 1, 1, 1, 1, 1, 1, 1, 8] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

%t Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] == 0 && IntegerQ[k^(1/3)]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 85}]

%Y Cf. A023358, A100346, A294105, A294333.

%Y Cf. A004709, A046099.

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Oct 28 2017