A285052 Number of idempotent equivalence classes for multiplication in Zn.

1, 4, 4, 4, 4, 16, 4, 4, 4, 16, 4, 16, 4, 16, 16, 4, 4, 16, 4, 16, 16, 16, 4, 16, 4, 16, 4, 16, 4, 64, 4, 4, 16, 16, 16, 16, 4, 16, 16, 16, 4, 64, 4, 16, 16, 16, 4, 16, 4, 16, 16, 16, 4, 16, 16, 16, 16, 16, 4, 64, 4, 16, 16, 4, 16, 64, 4, 16, 16, 64, 4, 16, 4, 16, 16, 16, 16, 64, 4, 16, 4, 16, 4, 64, 16, 16, 16, 16, 4, 64, 16

Offset

1,2

Comments

Consider triples (a,b,c) over Zn where a*b=c. Map each of the three elements to its idempotent under self multiplication, (g^i) * (g^i) = (g^i). Count the distinct triples.

Links

Table of n, a(n) for n=1..91.

Chad Brewbaker, Endoscope: A toolkit for analysis of endofunctions on small sets

Formula

Conjecture: a(n) = 4^A001221(n).

Example

For n=6: [(0,0,0),(0,1,0),(0,4,0),(0,3,0),(1,0,0),(1,1,1),(1,4,4),(1,3,3),(4,0,0),(4,1,4),(4,4,4),(4,3,0),(3,0,0),(3,1,3),(3,4,0),(3,3,3)], so a(6) = 16.

Crossrefs

Sequence in context: A294246 A107680 A358509 * A369719 A369757 A365489

Adjacent sequences: A285049 A285050 A285051 * A285053 A285054 A285055

Keyword

nonn

Author

Chad Brewbaker, Apr 08 2017

Status

approved