login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 25
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

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

EXAMPLE

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).

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A076664 A220477 A049939 * A240401 A133375 A057295

Adjacent sequences: A296299 A296300 A296301 * A296303 A296304 A296305

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 11 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)