A285055 Sum of the cycle lengths of the elements 0,1,...n-1, in Zn under multiplication.

1, 2, 4, 5, 12, 8, 22, 11, 24, 24, 64, 18, 78, 44, 38, 31, 172, 48, 184, 50, 74, 128, 334, 38, 236, 156, 192, 96, 474, 76, 442, 103, 214, 344, 194, 106, 672, 368, 242, 102, 904, 148, 904, 278, 218, 668, 1522, 102, 910, 472, 518, 320, 1728, 384, 558, 200, 614, 948

Offset: 1

Author

Chad Brewbaker, Apr 08 2017

Keywords

• nonn

Examples

			For n=3, 0->0 (cycle length 1), 1->1 (cycle length 1) and 2->1->2 (cycle length 2); 1+1+2 = 4.
The triangle of the cycle lengths is:
1 ;
1, 1 ;
1, 1, 2 ;
1, 1, 1, 2 ;
1, 1, 4, 4, 2 ;
1, 1, 2, 1, 1, 2 ;
1, 1, 3, 6, 3, 6, 2 ;
1, 1, 1, 2, 1, 2, 1, 2 ;
1, 1, 6, 1, 3, 6, 1, 3, 2 ;
1, 1, 4, 4, 2, 1, 1, 4, 4, 2 ;
		

Crossrefs

See A060014 for permutations on n elements.

Programs

Maple

A285055Tr := proc(n,m)
    local a,nmap,cyc ;
    nmap := n ;
    cyc := [n] ;
    for a from 1 do
        nmap := modp(nmap*n,m) ;
        if member(nmap,cyc,'i') then
            return nops(cyc)-i+1;
        else
            cyc := [op(cyc),nmap] ;
        end if;
    end do:
end proc:
A285055 := proc(m)
    add(A285055Tr(n,m),n=0..m-1) ;
end proc:
seq(A285055(m),m=1..30) ; # R. J. Mathar, May 06 2017