%I A014197
%S A014197 2,3,0,4,0,4,0,5,0,2,0,6,0,0,0,6,0,4,0,5,0,2,0,10,0,0,0,2,0,2,0,
%T A014197 7,0,0,0,8,0,0,0,9,0,4,0,3,0,2,0,11,0,0,0,2,0,2,0,3,0,2,0,9,0,0,
%U A014197 0,8,0,2,0,0,0,2,0,17,0,0,0,0,0,2,0,10,0,2,0,6,0,0,0,6,0,0,0,3
%N A014197 Number of numbers m with Euler phi(m) = n.
%C A014197 Carmichael conjectured that there are no 1's in this sequence.
%C A014197 Number of cyclotomic polynomials of degree n. - T. D. Noe (noe(AT)sspectra.com), 
               Aug 15 2003
%D A014197 R. K. Guy, Unsolved Problems in Number Theory, section B39.
%D A014197 J. Roberts, Lure of The Integers, entry 32, page 182.
%H A014197 T. D. Noe, <a href="b014197.txt">Table of n, a(n) for n = 1..10000</a>
%H A014197 K. Ford, <a href="http://arXiv.org/abs/math.NT/9907204">[math/9907204] 
               The number of solutions of phi(x)=m</a>
%H A014197 Primefan, <a href="http://primefan.tripod.com/TotientAnswers1000.html">
               Totient Answers For The First 1000 Integers</a>
%H A014197 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TotientFunction.html">Totient Function</a>
%H A014197 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TotientValenceFunction.html">Totient Valence Function</a>
%F A014197 Dirichlet g.f.: sum(n>=1, a(n)*n^-s)=zeta(s)*prod(1+1/(p-1)^s-1/p^s) 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 12 2003
%F A014197 lim n ->infinity (1/n)*sum(k=1, n, a(k))=zeta(2)*zeta(3)/zeta(6)=1.94359643682075920505707036... 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 12 2003
%p A014197 with(numtheory): A014197 := n-> nops(invphi(i));
%o A014197 (PARI) A014197(n,m=1) = { n==1 && return(1+(m<2)); my(p,q); sumdiv(n, 
               d, if( d>=m && isprime(d+1), sum( i=0,valuation(q=n\d,p=d+1), A014197(q\p^i,
               p))))} [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 05 2009]
%Y A014197 Cf. A058277, A002202, A032446.
%Y A014197 Cf. A070243 (partial sums).
%Y A014197 For records see A131934, A097942.
%Y A014197 Sequence in context: A122059 A164917 A166238 this_sequence A021438 A025638 
               A025639
%Y A014197 Adjacent sequences: A014194 A014195 A014196 this_sequence A014198 A014199 
               A014200
%K A014197 nonn,nice,easy
%O A014197 1,1
%A A014197 N. J. A. Sloane (njas(AT)research.att.com).
%E A014197 Additional comments from Jud McCranie (j.mccranie(AT)comcast.net), Oct 
               10 2000
%E A014197 Replaced a geocities.com URL - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 30 2009