A161787 Number of (undirected) cycles in the graph with nodes labeled 1..n, and nodes i and j joined by an edge if i divides j or vice versa.

0, 0, 0, 1, 1, 6, 6, 18, 25, 42, 42, 241, 241, 324, 667, 1602, 1602, 5511, 5511, 21596, 32549, 35434, 35434, 237727, 270992, 292057, 421656, 1140425, 1140425, 7609789, 7609789, 19163336, 22436043, 23293234, 46391754, 313698907, 313698907, 324745136, 370720970, 2113744875

Offset

1,6

Comments

Old definition was "Number of unique loops in a map of 1 to N vertices, with nondirectional connections between vertices which are factors or multiples of each other".

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

Example

From Andrew Howroyd, Aug 26 2017: (Start)
Case n=4: The only cycle is 1-2-4.
Case n=6: The 6 cycles are 1-2-4, 1-2-6, 1-3-6, 1-3-6-2, 1-3-6-2-4, 1-6-2-4.
(End)

Crossrefs

Sequence in context: A315824 A315825 A328528 * A342285 A092297 A294669

Adjacent sequences: A161784 A161785 A161786 * A161788 A161789 A161790

Keyword

nonn,obsc

Author

David Eaton (dave(AT)suave.net), Jun 19 2009

Extensions

Partially edited by N. J. A. Sloane, Dec 21 2014

Name clarified, a(21) corrected and a(25)-a(40) from Andrew Howroyd, Aug 26 2017

Status

approved