A063741 Smallest number whose inverse cototient set has n elements.

10, 0, 4, 8, 23, 35, 47, 59, 63, 83, 89, 113, 143, 119, 197, 167, 279, 233, 281, 209, 269, 323, 299, 359, 497, 329, 455, 605, 389, 461, 479, 419, 539, 599, 509, 755, 791, 713, 875, 797, 719, 629, 659, 1025, 1163, 929, 779, 1193, 1121, 899, 1133, 1091, 839

Offset: 0

Author

Labos Elemer, Aug 13 2001

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 0..1000

Crossrefs

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

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

Programs

Mathematica

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 *)

Formula

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

a(n) = min { k | A063740(k) = n }. - M. F. Hasler, Jan 11 2018

Extensions

More terms from David Wasserman, Jul 11 2002