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A196079
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Difference between the largest and smallest inverse of totient function.
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1
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1, 3, 7, 11, 15, 11, 29, 43, 35, 41, 23, 55, 29, 31, 69, 89, 109, 55, 69, 47, 145, 53, 81, 87, 59, 137, 155, 67, 71, 197, 79, 207, 83, 165, 187, 141, 323, 149, 103, 159, 107, 269, 121, 235, 177, 319, 127, 255, 131, 253, 137, 139, 213, 445, 149, 151
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OFFSET
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1,2
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COMMENTS
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No terms are zero if Carmichael's conjecture is true.
Even terms are rare: e.g., all inverses of 257*2^16 are even [Foster], so the difference between the largest and smallest inverse is even.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
William P. Wardlaw, L. L. Foster and R. J. Simpson, Problem E3361, Amer. Math. Monthly, Vol. 98, No. 5 (May, 1991), 443-444.
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FORMULA
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a(n) = A006511(n) - A002181(n).
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EXAMPLE
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Let n=3. The largest inverse of A002202(3)=4 is A006511(3)=12, the smallest inverse is A002181(3)=5, so a(3)=12-5=7.
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MATHEMATICA
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max = 300; inversePhi[_?OddQ] = {}; inversePhi[1] = {1, 2}; inversePhi[m_] := Module[{p, nmax, n, nn}, p = Select[Divisors[m] + 1, PrimeQ]; nmax = m*Times @@ (p/(p - 1)); n = m; nn = Reap[While[n <= nmax, If[EulerPhi[n] == m, Sow[n]]; n++]] // Last; If[nn == {}, {}, First[nn]]]; Join[{2}, Reap[For[n = 2, n <= max, n = n + 2, nn = inversePhi[n] ; If[ nn != {} , Sow[Max[nn] - Min[nn]]]]] // Last // First] (* Jean-François Alcover, Nov 21 2013 *)
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CROSSREFS
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Cf. A002181, A002202, A006511.
Sequence in context: A310208 A168285 A310209 * A285497 A079710 A145832
Adjacent sequences: A196076 A196077 A196078 * A196080 A196081 A196082
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KEYWORD
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nonn
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AUTHOR
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Franz Vrabec, Sep 27 2011
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EXTENSIONS
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a(1) corrected by the editors, Nov 23 2013
a(1) in b-file corrected by Andrew Howroyd, Feb 22 2018
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STATUS
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approved
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