A063507 Least k such that k - phi(k) = n, or 0 if no such k exists.

2, 4, 9, 6, 25, 10, 15, 12, 21, 0, 35, 18, 33, 26, 39, 24, 65, 34, 51, 38, 45, 30, 95, 36, 69, 0, 63, 52, 161, 42, 87, 48, 93, 0, 75, 54, 217, 74, 99, 76, 185, 82, 123, 60, 117, 66, 215, 72, 141, 0, 235, 0, 329, 78, 159, 98, 105, 0, 371, 84, 177, 122, 135, 96, 305, 90, 427

Offset: 1

Author

Labos Elemer, Aug 09 2001

Keywords

• nonn

Comments

Inverse cototient (A051953) sets represented by their minimum, as in A002181 for totient function. Impossible values (A005278) are replaced by zero.

If a(n) > 0, then it appears that a(n) > 1.26n. - T. D. Noe, Dec 06 2006

Examples

			x = InvCototient[24] = {36, 40, 44, 46}; Phi[x] = Phi[{36, 40, 44, 46}] = {12, 16, 20, 22}; x-Phi[x] = {24, 24, 24, 24}, so a(24) = Min[InvCototient[24]]; a(10) = 0 because 10 is in A005278.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A051953, A000010, A002181, A005277, A005278.

Cf. A063748 (greatest solution to x-phi(x)=n).

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

Programs

Mathematica

Table[SelectFirst[Range[n^2 + 1], # - EulerPhi[#] == n &] /. k_ /; ! IntegerQ@ k -> 0, {n, 67}] (* Michael De Vlieger, Jan 11 2018 *)

Formula

a(n)-A051953(a(n)) = n if possible and a(n)=0 if n belongs to A005278.

Extensions

Edited by N. J. A. Sloane, Oct 25 2008 at the suggestion of R. J. Mathar