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 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). 10
 1, 2, 4, 8, 12, 24, 48, 72, 144, 240, 432, 480, 576, 720, 1152, 1440, 2880, 4320, 5760, 8640, 11520, 17280, 25920, 30240, 34560, 40320, 51840, 60480, 69120, 80640, 103680, 120960, 161280, 181440, 207360, 241920, 362880, 483840, 725760, 967680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If you inspect PhiAnsYldList after running the Mathematica program below, the zeros with even-numbered indices should correspond to the nontotients (A005277). Where records occur in A014197. - T. D. Noe, Jun 13 2006 Cf. A131934. LINKS Jud McCranie, Table of n, a(n) for n = 1..109 (first 79 terms from T. D. Noe and terms n = 80..86 from Donovan Johnson) Wikipedia, Highly totient number EXAMPLE 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}. MAPLE HighlyTotientNumbers := proc(n) # n > 1 is search maximum local L, m, i, r; L := NULL; m := 0; for i from 1 to n do   r := nops(numtheory[invphi](i));   if r > m then L := L, [i, r]; m := r fi od; [L] end: A097942_list := n -> seq(s[1], s = HighlyTotientNumbers(n)); A097942_list(500); # Peter Luschny, Sep 01 2012 MATHEMATICA 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] PROG (Sage) def HighlyTotientNumbers(n) : # n > 1 is search maximum.     R = {}     for i in (1..n^2) :         r = euler_phi(i)         if r <= n :             R[r] = R[r] + 1 if r in R else 1     # print R.keys()   # A002202     # print R.values() # A058277     P = []; m = 1     for l in sorted(R.keys()) :         if R[l] > m : m = R[l]; P.append((l, m))     # print [l[0] for l in P] # A097942     # print [l[1] for l in P] # A131934     return P A097942_list = lambda n: [s[0] for s in HighlyTotientNumbers(n)] A097942_list(500) # Peter Luschny, Sep 01 2012 (PARI) { A097942_list(n) = local(L, m, i, r);   m = 0;   for(i=1, n, \\ from Max Alekseyev, http://home.gwu.edu/~maxal/gpscripts/    r = numinvphi(i);    if(r > m, print1(i, ", "); m = r) ); } \\ Peter Luschny, Sep 01 2012 CROSSREFS A subsequence of A007374. Cf. A000010, A005277, A014573, A004653, A105207, A105208. Sequence in context: A279312 A326076 A181808 * A004653 A115386 A306491 Adjacent sequences:  A097939 A097940 A097941 * A097943 A097944 A097945 KEYWORD nonn AUTHOR Alonso del Arte, Sep 05 2004 EXTENSIONS Edited and extended by Robert G. Wilson v, Sep 07 2004 STATUS approved

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Last modified October 20 02:54 EDT 2019. Contains 328244 sequences. (Running on oeis4.)