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

1,2

Links

Table of n, a(n) for n=1..58.

Example

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 ;

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

Crossrefs

See A060014 for permutations on n elements.

Sequence in context: A317828 A293274 A101961 * A344712 A351753 A268530

Adjacent sequences: A285052 A285053 A285054 * A285056 A285057 A285058

Keyword

nonn

Author

Chad Brewbaker, Apr 08 2017

Status

approved