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A196079 Difference between the largest and smallest inverse of totient function.

%I A196079 #26 Feb 23 2018 09:29:50
%S A196079 1,3,7,11,15,11,29,43,35,41,23,55,29,31,69,89,109,55,69,47,145,53,81,
%T A196079 87,59,137,155,67,71,197,79,207,83,165,187,141,323,149,103,159,107,
%U A196079 269,121,235,177,319,127,255,131,253,137,139,213,445,149,151
%N A196079 Difference between the largest and smallest inverse of totient function.
%C A196079 No terms are zero if Carmichael's conjecture is true.
%C A196079 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.
%H A196079 T. D. Noe, <a href="/A196079/b196079.txt">Table of n, a(n) for n = 1..10000</a>
%H A196079 William P. Wardlaw, L. L. Foster and R. J. Simpson, <a href="http://www.jstor.org/stable/2323869">Problem E3361</a>, Amer. Math. Monthly, Vol. 98, No. 5 (May, 1991), 443-444.
%F A196079 a(n) = A006511(n) - A002181(n).
%e A196079 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.
%t A196079 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 *)
%Y A196079 Cf. A002181, A002202, A006511.
%K A196079 nonn
%O A196079 1,2
%A A196079 _Franz Vrabec_, Sep 27 2011
%E A196079 a(1) corrected by the editors, Nov 23 2013
%E A196079 a(1) in b-file corrected by _Andrew Howroyd_, Feb 22 2018