

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
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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), 443444.


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)=125=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] (* JeanFrançois 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 bfile corrected by Andrew Howroyd, Feb 22 2018


STATUS

approved



