%I #24 Jan 22 2018 16:08:01

%S 10,0,4,8,23,35,47,59,63,83,89,113,143,119,197,167,279,233,281,209,

%T 269,323,299,359,497,329,455,605,389,461,479,419,539,599,509,755,791,

%U 713,875,797,719,629,659,1025,1163,929,779,1193,1121,899,1133,1091,839

%N Smallest number whose inverse cototient set has n elements.

%C Note that 1 is the only number that has infinitely many cototient-inverses, namely, all the primes.

%H Donovan Johnson, <a href="/A063741/b063741.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = min {x: |InvCot(x)| = n}.

%F a(n) = min { k | A063740(k) = n }. - _M. F. Hasler_, Jan 11 2018

%e For n = 1, 2, 3, 4, 5, ..., the corresponding inverse sets are as follows: {}, {4}, {6, 8}, {12, 14, 16}, {95, 119, 143, 529}, {75, 155, 203, 299, 323}, ..., {455, 815, 1727, 2567, 2831, 4031, 4247, 4847, 5207, 6431, 6527, 6767, 6887, 7031, 27889}, including 0, 1, 2, 3, 4, 5, ..., 15 numbers.

%t With[{s = Array[Count[Range[#^2], k_ /; k - EulerPhi@ k == #] &, 300, 2]}, ReplacePart[TakeWhile[First@ FirstPosition[s, #] + 1 & /@ Range[0, Max@ s], IntegerQ], 2 -> 0]] (* _Michael De Vlieger_, Jan 11 2018 *)

%Y Cf. A000010, A051953 (cototient: n - phi(n)), A063507.

%Y Cf. A063740 (number of k such that cototient(k) = n).

%K nonn

%O 0,1

%A _Labos Elemer_, Aug 13 2001

%E More terms from _David Wasserman_, Jul 11 2002