A196079 - OEIS

A196079

Difference between the largest and smallest inverse of totient function.

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

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 A373415

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