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
Keywords
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
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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