%I A051953
%S A051953 0,1,1,2,1,4,1,4,3,6,1,8,1,8,7,8,1,12,1,12,9,12,1,16,5,14,9,16,1,22,1,
%T A051953 16,13,18,11,24,1,20,15,24,1,30,1,24,21,24,1,32,7,30,19,28,1,36,15,32,
%U A051953 21,30,1,44,1,32,27,32,17,46,1,36,25,46,1,48,1,38,35,40,17,54,1,48,27
%N A051953 Cototient(n) := n - phi(n).
%C A051953 Unlike totients, cototient[x+1] = cototient[x] never holds - except 2-Phi[2] 
               = 3-Phi[3] = 1 - because cototient[x] congruent x modulo 2. - Labos 
               E. (labos(AT)ana.sote.hu), Aug 08 2001
%D A051953 J. Browkin and A. Schinzel, On integers not of the form n-phi(n), Colloq. 
               Math., 68 (1995), 55-58.
%D A051953 R. E. Jamison, The Helly bound for singular sums, Discrete Math., 249 
               (2002), 117-133.
%H A051953 T. D. Noe, <a href="b051953.txt">Table of n, a(n) for n = 1..10000</a>
%F A051953 Equals Mobius transform (A054525) of A001065. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jul 11 2008
%F A051953 a(n) = n - A000010(n). [From Omar E. Pol (info(AT)polprimos.com), Dec 
               23 2008]
%e A051953 n=12, Phi[12]=4=Card[{1,5,7,11}], a[12]=12-Phi[12]=8, numbers not exceeding 
               12 and not coprime to 12:{2,3,4,6,8,9,10,12}
%p A051953 with(numtheory); A051953 := n->n-phi(n);
%Y A051953 Cf. A000010, A005278, A001274, A098006.
%Y A051953 Cf. A054525, A001065.
%Y A051953 Sequence in context: A112350 A063717 A024994 this_sequence A079277 A066452 
               A007104
%Y A051953 Adjacent sequences: A051950 A051951 A051952 this_sequence A051954 A051955 
               A051956
%K A051953 nonn,easy,nice
%O A051953 1,4
%A A051953 Labos E. (labos(AT)ana.sote.hu), Dec 21 1999