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.

1, 0, 2, 5, 14, 24, 62, 114, 249, 480, 1022, 1978, 4094, 8064, 16348, 32520, 65534, 130512, 262142, 523270, 1048444, 2095104, 4194302, 8384316, 16777185, 33546240, 67108356, 134201398, 268435454, 536837136, 1073741822, 2147418240, 4294965244, 8589803520

Offset: 1

Author

Gus Wiseman, Dec 11 2017

Keywords

• nonn

Examples

			The a(6) = 24 aperiodic compositions with relatively prime parts are:
(15), (51),
(114), (123), (132), (141), (213), (231), (312), (321), (411),
(1113), (1122), (1131), (1221), (1311), (2112), (2211), (3111),
(11112), (11121), (11211), (12111), (21111).
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000740, A000837, A007427, A008683, A008965, A059966, A060223, A100953, A228369, A281013.

Programs

Mathematica

Table[DivisorSum[n,Function[d,MoebiusMu[n/d]*DivisorSum[d,MoebiusMu[#]*2^(d/#-1)&]]],{n,20}]

Formula

a = mu * mu * c, where * is Dirichlet convolution and c(n) = 2^(n-1).