This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A140185 Number of connected groupoids (categories all of whose morphisms are invertible) with n morphisms. 4
 1, 1, 1, 1, 3, 1, 2, 1, 6, 3, 2, 1, 6, 1, 2, 1, 17, 1, 6, 1, 6, 2, 2, 1, 17, 3, 2, 6, 5, 1, 4, 1, 57, 1, 2, 1, 19, 1, 2, 2, 16, 1, 6, 1, 5, 3, 2, 1, 58, 3, 6, 1, 6, 1, 17, 2, 15, 2, 2, 1, 14, 1, 2, 5, 284, 1, 4, 1, 6, 1, 4, 1, 61, 1, 2, 4, 5, 1, 6, 1, 58, 18, 2, 1, 17, 1, 2, 1, 14, 1, 12, 1, 5, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n) >= A000001(n) (number of groups of order n), with equality if and only if n is squarefree (sequence A005117). LINKS B. Jubin, Sequences contributed to the OEIS. FORMULA a(0) = 1 and if n>0, a(n) = sum(A000001(n/(k^2)),k^2|n). Indeed, if b(n,k) is the number of connected groupoids with n morphisms and k objects, then the only nonzero values are b(0,0) = 1 and b(m.k^2,k) = A000001(m) with m,k>0. CROSSREFS Cf. A140186, A140187, A140188, A140189. Sequence in context: A010123 A039620 A008296 * A229341 A106790 A078897 Adjacent sequences:  A140182 A140183 A140184 * A140186 A140187 A140188 KEYWORD nonn AUTHOR Benoit Jubin, May 12 2008 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.

Last modified December 6 19:22 EST 2019. Contains 329809 sequences. (Running on oeis4.)