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A300702 Number of compositions (ordered partitions) of n into parts that do not divide n.

%I A300702 #8 Mar 11 2018 17:28:48
%S A300702 1,0,0,0,0,2,0,7,2,7,7,54,2,143,33,47,30,986,23,2583,58,1018,828,
%T A300702 17710,32,23866,3917,14586,1368,317810,248,832039,5902,188953,85038,
%U A300702 1505979,602,14930351,393663,2350986,13524,102334154,16401,267914295,431711,4438212,8400611,1836311902
%N A300702 Number of compositions (ordered partitions) of n into parts that do not divide n.
%H A300702 Alois P. Heinz, <a href="/A300702/b300702.txt">Table of n, a(n) for n = 0..2000</a>
%H A300702 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A300702 a(7) = 7 because we have [5, 2], [4, 3], [3, 4], [3, 2, 2], [2, 5], [2, 3, 2] and [2, 2, 3].
%p A300702 a:= proc(m) option remember; local b; b:= proc(n)
%p A300702       option remember; `if`(n=0, 1, add(`if`(
%p A300702       irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
%p A300702     end:
%p A300702 seq(a(n), n=0..60);  # _Alois P. Heinz_, Mar 11 2018
%t A300702 Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 47}]
%Y A300702 Cf. A011782, A098743, A100346, A200745.
%K A300702 nonn
%O A300702 0,6
%A A300702 _Ilya Gutkovskiy_, Mar 11 2018