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A300706 Number of compositions (ordered partitions) of n into squarefree parts that do not divide n.

%I A300706 #11 Mar 16 2018 10:59:07
%S A300706 1,0,0,0,0,2,0,5,2,5,2,27,2,67,12,16,28,366,4,848,28,182,153,4591,20,
%T A300706 4172,554,2217,558,57695,6,134118,3834,14629,6972,97478,258,1684852,
%U A300706 24467,120869,5308,9104710,189,21165023,124427,117017,297830,114373157,3394,126979537,72158,7655405
%N A300706 Number of compositions (ordered partitions) of n into squarefree parts that do not divide n.
%H A300706 Alois P. Heinz, <a href="/A300706/b300706.txt">Table of n, a(n) for n = 0..2000</a>
%H A300706 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A300706 a(18) = 4 because we have [13, 5], [11, 7], [7, 11] and [5, 13].
%p A300706 with(numtheory):
%p A300706 a:= proc(m) option remember; local b; b:= proc(n) option
%p A300706       remember; `if`(n=0, 1, add(`if`(not issqrfree(j) or
%p A300706        irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
%p A300706     end:
%p A300706 seq(a(n), n=0..70);  # _Alois P. Heinz_, Mar 11 2018
%t A300706 Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && SquareFreeQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 51}]
%Y A300706 Cf. A005117, A280194, A284464, A300585, A300586, A300702, A300703, A300704.
%K A300706 nonn
%O A300706 0,6
%A A300706 _Ilya Gutkovskiy_, Mar 11 2018