%I A003557
%S A003557 1,1,1,2,1,1,1,4,3,1,1,2,1,1,1,8,1,3,1,2,1,1,1,4,5,1,9,2,1,1,1,16,1,
%T A003557 1,1,6,1,1,1,4,1,1,1,2,3,1,1,8,7,5,1,2,1,9,1,4,1,1,1,2,1,1,3,32,1,1,
%U A003557 1,2,1,1,1,12,1,1,5,2,1,1,1,8,27,1,1,2,1,1,1,4,1,3,1,2,1,1,1,16,1,7
%N A003557 n divided by largest square-free divisor of n.
%C A003557 a(n) is the size of the Frattini subgroup of the cyclic group C_n - Ahmed 
               Fares (ahmedfares(AT)my-deja.com), Jun 07 2001. Also of the Frattini 
               subgroup of the dihedral group with 2*n elements. - Sharon Sela (sharonsela(AT)hotmail.com), 
               Jan 01 2002
%C A003557 Number of solutions to x^m==0 (mod n) provided that n < 2^(m+1), i.e. 
               the sequence of sequences A000188, A000189, A000190, etc. converges 
               to this sequence. - Henry Bottomley (se16(AT)btinternet.com), Sep 
               18 2001
%C A003557 a(n) is the number of nilpotent elements in the ring Z/nZ. - Laszlo Toth 
               (ltoth(AT)ttk.pte.hu), May 22 2009
%C A003557 The sequence of partial products of a(n) is A085056(n). [From Peter Luschny 
               (peter(AT)luschny.de), Jun 29 2009]
%H A003557 R. Zumkeller, <a href="b003557.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A003557 H. Bottomley, <a href="http://www.gallup.unm.edu/~smarandache/math.htm">
               Some Smarandache-type multiplicative sequences</a>
%H A003557 S. R. Finch, <a href="http://arXiv.org/abs/math.NT/0605019">Idempotents 
               and Nilpotents Modulo n</a> (arXiv:math.NT/0605019)
%F A003557 Multiplicative with a(p^e) = p^(e-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jul 23 2001
%p A003557 Contribution from Peter Luschny (peter(AT)luschny.de), Jun 29 2009: (Start)
%p A003557 A003557 := proc(n) local A, p, i, j, h, q;
%p A003557 A := [seq(j,j=1..n)]; p := 2;
%p A003557 while p <= n do for j from p by p to n do
%p A003557 if irem(A[j], p, 'q') = 0 then A[j] := q fi od;
%p A003557 p := nextprime(p) od; A end:
%p A003557 (End)
%t A003557 Prepend[ Array[ #/Times@@(First[ Transpose[ FactorInteger[ # ] ] ])&, 
               100, 2 ], 1 ]
%Y A003557 Cf. A007947, A062378, A062379.
%Y A003557 Sequence in context: A104445 A000189 A000190 this_sequence A073752 A128708 
               A087653
%Y A003557 Adjacent sequences: A003554 A003555 A003556 this_sequence A003558 A003559 
               A003560
%K A003557 nonn,easy,mult
%O A003557 1,4
%A A003557 Marc LeBrun (mlb(AT)well.com)
%E A003557 Program added Apr 10, 1997 (og).