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

Author

Chad Brewbaker, Apr 08 2017

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Formula

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