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

1,2

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

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 *)

Prog

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

Crossrefs

Cf. A000010, A000384, A051953.

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

Sequence in context: A064627 A324813 A235050 * A169802 A194948 A266679

Adjacent sequences: A117283 A117284 A117285 * A117287 A117288 A117289

Keyword

nonn

Author

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

Extensions

Corrected by T. D. Noe, Oct 25 2006

Status

approved