A117284 Numbers k for which the cototient k-phi(k) is a triangular number.

1, 2, 3, 5, 7, 9, 10, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 45, 47, 52, 53, 54, 55, 57, 59, 61, 67, 68, 71, 73, 79, 83, 85, 89, 90, 97, 101, 103, 107, 109, 113, 114, 117, 127, 129, 131, 137, 139, 149, 151, 157, 159, 163, 167, 168, 173, 175, 179, 181, 191, 193

Offset: 1

Author

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

Keywords

• nonn

Examples

			39 is in the sequence because 39-phi(39) = 15, which is a triangular number.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1001 from Harvey P. Dale)

Crossrefs

Cf. A000010, A000217, A051953.

Cf. A117283, A117285, A117286, A117287, A117288, A117289.

Programs

Mathematica

Select[Range[200],OddQ[Sqrt[8(#-EulerPhi[#])+1]]&] (* Harvey P. Dale, Jun 29 2015 *)

PARI

isok(n) = ispolygonal(n - eulerphi(n), 3); \\ Michel Marcus, Feb 26 2014

Extensions

Offset corrected by Amiram Eldar, Mar 23 2021