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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069626 Number of distinct sets of numbers whose least common multiple is n. 3
1, 1, 1, 2, 1, 5, 1, 4, 2, 5, 1, 22, 1, 5, 5, 8, 1, 22, 1, 22, 5, 5, 1, 92, 2, 5, 4, 22, 1, 109, 1, 16, 5, 5, 5, 200, 1, 5, 5, 92, 1, 109, 1, 22, 22, 5, 1, 376, 2, 22, 5, 22, 1, 92, 5, 92, 5, 5, 1, 1874, 1, 5, 22, 32, 5, 109, 1, 22, 5, 109, 1, 1696, 1, 5, 22, 22, 5, 109, 1, 376, 8, 5, 1, 1874, 5, 5, 5, 92, 1, 1874, 5, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

(1,n) counts as one such set and 1 may not occur in any other set.

a(p) = 1, a(p*q) = 5, a(p^2*q) = 13, a(p^3) = 4, a(p^4) = 8 etc. where p and q are primes. It can be shown that a(p^k) = 2^(k-1). Problem: find an expression for a(N) when N = p^a*q^b*r^c*..., p,q,r are primes.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{ d divides n } mu(n/d)*2^(tau(d)-1). - Vladeta Jovovic, Jul 07 2003

EXAMPLE

a(6) = 5 as the five distinct sets are (1, 6), (2, 6), (3, 6), (2, 3) and (2, 3, 6).

a(12) = 22 from (1,12), (4,3), (2,4,3), (4,6), (2,4,6), (4,3,6), (2,4,3,6), (2,12), (4,12), (2,4,12), (3,12), (2,3,12), (4,3,12), (2,4,3,12), (6,12), (2,6,12), (4,6,12), (2,4,6,12), (3,6,12), (2,3,6,12), (4,3,6,12), (2,4,3,6,12).

MATHEMATICA

a[n_] := Sum[ MoebiusMu[n/d] * 2^(DivisorSigma[0, d] - 1), {d, Divisors[n]}]; Table[a[n], {n, 1, 92}](* Jean-Fran├žois Alcover, Nov 30 2011, after Vladeta Jovovic *)

PROG

(Haskell)  -- following Vladeta Jovovic's formula.

a069626 n = sum $

   map (\d -> (a008683 (n `div` d)) * 2 ^ (a000005 d - 1)) $ a027750_row n

-- Reinhard Zumkeller, Jun 12 2015, Feb 07 2011

CROSSREFS

Sequence in context: A055205 A161686 A289621 * A249274 A205443 A069359

Adjacent sequences:  A069623 A069624 A069625 * A069627 A069628 A069629

KEYWORD

nonn,nice,easy

AUTHOR

Amarnath Murthy, Mar 27 2002

EXTENSIONS

Corrected and extended by Naohiro Nomoto, Apr 25 2002

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 16 11:10 EDT 2019. Contains 327095 sequences. (Running on oeis4.)