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Search: id:A097942
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| A097942 |
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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). |
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+0
8
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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If you inspect PhiAnsYldList after running the program below, the zeros with even-numbered indices should correspond to the nontotients (A005277).
Where records occur in A014197. - T. D. Noe (noe(AT)sspectra.com), Jun 13 2006. Cf. A131934.
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LINKS
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Wikipedia, Highly totient number
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EXAMPLE
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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}.
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MATHEMATICA
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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]
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CROSSREFS
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A subsequence of A007374.
Cf. A000010, A005277, A014573, A004653, A105207, A105208.
Sequence in context: A032473 A084422 A089821 this_sequence A004653 A115386 A058771
Adjacent sequences: A097939 A097940 A097941 this_sequence A097943 A097944 A097945
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KEYWORD
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nonn
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AUTHOR
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Alonso Delarte (alonso.delarte(AT)gmail.com), Sep 05 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 07 2004
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