login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A133732 A054525 * A000041. 2
1, 0, 1, 2, 4, 5, 10, 12, 20, 25, 41, 47, 76, 90, 129, 161, 230, 270, 384, 458, 615, 750, 1001, 1187, 1570, 1881, 2414, 2907, 3717, 4400, 5603, 6666, 8306, 9912, 12295, 14537, 17976, 21252, 25937, 30683, 37337, 43861, 53173, 62467, 75020, 88132 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A000041 = (1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, ...).

LINKS

Table of n, a(n) for n=1..46.

Mircea Merca and Maxie D. Schmidt, Generating Special Arithmetic Functions by Lambert Series Factorizations, arXiv:1706.00393 [math.NT], 2017. See Conjecture 3.1.

FORMULA

Möbius transform of A000041, the partition numbers.

EXAMPLE

a(4) = 2 = (0, -1, 0, 1) dot (1, 1, 2, 3) = (0, -1, 0, 3).

MAPLE

read("transforms") : A000041 := proc(n) combinat[numbpart](n) ; end: a000041 := [seq(A000041(n), n=0..150)] ; a133732 := MOBIUS(a000041) ; # R. J. Mathar, Jan 19 2009

mob := (m, n) -> if irem(m, n) = 0 then numtheory:-mobius(m/n) else 0 fi:

A133732 := n -> add(mob(n, d)*combinat:-numbpart(d-1), d=1..n):

seq(A133732(n), n=1..46); # Peter Luschny, Jan 20 2018

MATHEMATICA

a[n_] := DivisorSum[n, MoebiusMu[n/#]*PartitionsP[#-1]&];

Table[a[n], {n, 1, 45}] (* Jean-François Alcover, Jan 20 2018 *)

CROSSREFS

Cf. A054525.

Sequence in context: A260385 A022944 A241822 * A128215 A097132 A013578

Adjacent sequences:  A133729 A133730 A133731 * A133733 A133734 A133735

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Sep 22 2007

EXTENSIONS

More terms from R. J. Mathar, Jan 19 2009

Offset set to 1 by Peter Luschny, Jan 20 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 16 15:26 EST 2018. Contains 317274 sequences. (Running on oeis4.)