A117286 Numbers k for which the cototient k-phi(k) is a hexagonal number.

1, 2, 3, 5, 7, 10, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 47, 52, 53, 55, 59, 61, 67, 71, 73, 79, 83, 89, 90, 97, 101, 103, 107, 109, 113, 117, 127, 129, 131, 137, 139, 149, 151, 157, 163, 167, 168, 173, 179, 181, 191, 193, 197, 199, 200, 205, 211, 223, 227, 229

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006

Keywords

• nonn

Comments

55 is in the sequence because 55-phi(55) = 15, which is a hexagonal number.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000384, A051953.

Cf. A117283, A117284, A117285, A117287, A117288, A117289.

Programs

Mathematica

cthQ[n_]:=Module[{c=n-EulerPhi[n]},IntegerQ[(Sqrt[1+8c]+1)/4]]; Join[{1}, Select[Range[250],cthQ]] (* Harvey P. Dale, Jan 16 2012 *)

PARI

isok(n) = ispolygonal(n - eulerphi(n), 6); \\ Michel Marcus, Feb 26 2014

Extensions

Corrected by T. D. Noe, Oct 25 2006