%I A097942
%S A097942 1,2,4,8,12,24,48,72,144,240,432,480,576,720,1152,1440,2880,4320,5760,
%T A097942 8640,11520,17280,25920,30240,34560,40320,51840,60480,69120,80640,
%U A097942 103680,120960,161280,181440,207360,241920,362880,483840,725760,967680
%N A097942 Highly totient numbers: each number k on this list has more solutions 
               to the equation phi(x) = k than any preceding k (where phi is Euler's 
               totient function, A000010).
%C A097942 If you inspect PhiAnsYldList after running the program below, the zeros 
               with even-numbered indices should correspond to the nontotients (A005277).
%C A097942 Where records occur in A014197. - T. D. Noe (noe(AT)sspectra.com), Jun 
               13 2006. Cf. A131934.
%H A097942 Wikipedia, <a href="http://en.wikipedia.org/wiki/Highly_totient_number">
               Highly totient number</a>
%e A097942 a(4) = 8 since phi(x) = 8 has the solutions {15, 16, 20, 24, 30}, one 
               more solution than a(3) = 4 for which phi(x) = 4 has solutions {5, 
               8, 10, 12}.
%t A097942 SearchMax = 2000; PhiAnsYldList = Table[0, {SearchMax}]; Do[PhiAns = 
               EulerPhi[m]; If[PhiAns <= SearchMax, PhiAnsYldList[[PhiAns]]++ ], 
               {m, 1, SearchMax^2}]; HighlyTotientList = {1}; CurrHigh = 1; Do[If[PhiAnsYldList[[n]] 
               > PhiAnsYldList[[CurrHigh]], HighlyTotientList = {HighlyTotientList, 
               n}; CurrHigh = n], {n, 2, SearchMax}]; Flatten[HighlyTotientList]
%Y A097942 A subsequence of A007374.
%Y A097942 Cf. A000010, A005277, A014573, A004653, A105207, A105208.
%Y A097942 Sequence in context: A032473 A084422 A089821 this_sequence A004653 A115386 
               A058771
%Y A097942 Adjacent sequences: A097939 A097940 A097941 this_sequence A097943 A097944 
               A097945
%K A097942 nonn
%O A097942 1,2
%A A097942 Alonso Delarte (alonso.delarte(AT)gmail.com), Sep 05 2004
%E A097942 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 07 
               2004