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A296302 Number of aperiodic compositions of n with relatively prime parts. Number of compositions of n with relatively prime parts and relatively prime run-lengths.

%I A296302 #25 Dec 19 2017 02:40:53
%S A296302 1,0,2,5,14,24,62,114,249,480,1022,1978,4094,8064,16348,32520,65534,
%T A296302 130512,262142,523270,1048444,2095104,4194302,8384316,16777185,
%U A296302 33546240,67108356,134201398,268435454,536837136,1073741822,2147418240,4294965244,8589803520
%N A296302 Number of aperiodic compositions of n with relatively prime parts. Number of compositions of n with relatively prime parts and relatively prime run-lengths.
%H A296302 Robert G. Wilson v, <a href="/A296302/b296302.txt">Table of n, a(n) for n = 1..1000</a>
%F A296302 a = mu * mu * c, where * is Dirichlet convolution and c(n) = 2^(n-1).
%e A296302 The a(6) = 24 aperiodic compositions with relatively prime parts are:
%e A296302 (15), (51),
%e A296302 (114), (123), (132), (141), (213), (231), (312), (321), (411),
%e A296302 (1113), (1122), (1131), (1221), (1311), (2112), (2211), (3111),
%e A296302 (11112), (11121), (11211), (12111), (21111).
%t A296302 Table[DivisorSum[n,Function[d,MoebiusMu[n/d]*DivisorSum[d,MoebiusMu[#]*2^(d/#-1)&]]],{n,20}]
%Y A296302 Cf. A000005, A000740, A000837, A007427, A008683, A008965, A059966, A060223, A100953, A228369, A281013.
%K A296302 nonn
%O A296302 1,3
%A A296302 _Gus Wiseman_, Dec 11 2017