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