login
A285052
Number of idempotent equivalence classes for multiplication in Zn.
2
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.
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
KEYWORD
nonn
AUTHOR
Chad Brewbaker, Apr 08 2017
STATUS
approved