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 A196079 Difference between the largest and smallest inverse of totient function. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS 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. FORMULA a(n) = A006511(n) - A002181(n). EXAMPLE 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. MATHEMATICA 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 *) CROSSREFS Cf. A002181, A002202, A006511. Sequence in context: A310208 A168285 A310209 * A285497 A079710 A145832 Adjacent sequences: A196076 A196077 A196078 * A196080 A196081 A196082 KEYWORD nonn AUTHOR Franz Vrabec, Sep 27 2011 EXTENSIONS a(1) corrected by the editors, Nov 23 2013 a(1) in b-file corrected by Andrew Howroyd, Feb 22 2018 STATUS approved

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Last modified March 28 23:19 EDT 2023. Contains 361596 sequences. (Running on oeis4.)