cp's OEIS Frontend

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

%I A285055 #10 May 10 2017 05:32:30
%S A285055 1,2,4,5,12,8,22,11,24,24,64,18,78,44,38,31,172,48,184,50,74,128,334,
%T A285055 38,236,156,192,96,474,76,442,103,214,344,194,106,672,368,242,102,904,
%U A285055 148,904,278,218,668,1522,102,910,472,518,320,1728,384,558,200,614,948
%N A285055 Sum of the cycle lengths of the elements 0,1,...n-1, in Zn under multiplication.
%e A285055 For n=3, 0->0 (cycle length 1), 1->1 (cycle length 1) and 2->1->2 (cycle length 2); 1+1+2 = 4.
%e A285055 The triangle of the cycle lengths is:
%e A285055 1 ;
%e A285055 1, 1 ;
%e A285055 1, 1, 2 ;
%e A285055 1, 1, 1, 2 ;
%e A285055 1, 1, 4, 4, 2 ;
%e A285055 1, 1, 2, 1, 1, 2 ;
%e A285055 1, 1, 3, 6, 3, 6, 2 ;
%e A285055 1, 1, 1, 2, 1, 2, 1, 2 ;
%e A285055 1, 1, 6, 1, 3, 6, 1, 3, 2 ;
%e A285055 1, 1, 4, 4, 2, 1, 1, 4, 4, 2 ;
%p A285055 A285055Tr := proc(n,m)
%p A285055     local a,nmap,cyc ;
%p A285055     nmap := n ;
%p A285055     cyc := [n] ;
%p A285055     for a from 1 do
%p A285055         nmap := modp(nmap*n,m) ;
%p A285055         if member(nmap,cyc,'i') then
%p A285055             return nops(cyc)-i+1;
%p A285055         else
%p A285055             cyc := [op(cyc),nmap] ;
%p A285055         end if;
%p A285055     end do:
%p A285055 end proc:
%p A285055 A285055 := proc(m)
%p A285055     add(A285055Tr(n,m),n=0..m-1) ;
%p A285055 end proc:
%p A285055 seq(A285055(m),m=1..30) ; # _R. J. Mathar_, May 06 2017
%Y A285055 See A060014 for permutations on n elements.
%K A285055 nonn
%O A285055 1,2
%A A285055 _Chad Brewbaker_, Apr 08 2017