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A140187 Number of connected groupoids (categories all of whose morphisms are invertible) with n times as many morphisms as objects. 2
1, 2, 3, 3, 5, 3, 6, 3, 10, 5, 6, 3, 13, 3, 6, 5, 24, 3, 13, 3, 13, 6, 6, 3, 33, 5, 6, 10, 12, 3, 14, 3, 75, 5, 6, 5, 34, 3, 6, 6, 32, 3, 17, 3, 12, 9, 6, 3, 99, 5, 13, 5, 13, 3, 33, 6, 30, 6, 6, 3, 39, 3, 6, 12, 342, 5, 14, 3, 13, 5, 14, 3, 104, 3, 6, 10, 12, 5, 17, 3, 98, 25, 6, 3, 43, 5, 6, 5, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
If n>1, a(n) >= 2 + A000001(n) (number of groups of order n), with equality if and only if n is prime (sequence A000040).
LINKS
FORMULA
a(n) = sum(A000001(n/k),k|n). (see formula for A140185)
a(n) = 1 + sum(A000001(n/k),k|n). (the 1 accounts for the empty groupoid; see formula for A140185)
CROSSREFS
Sequence in context: A279931 A071049 A171637 * A214127 A111607 A327124
KEYWORD
nonn
AUTHOR
Benoit Jubin, May 12 2008, May 16 2008
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)