A117288 Numbers k for which the cototient k-phi(k) is an octagonal number.

1, 2, 3, 5, 7, 11, 12, 13, 14, 16, 17, 19, 23, 29, 31, 37, 41, 43, 45, 47, 53, 57, 59, 61, 67, 71, 73, 76, 79, 83, 85, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 144, 149, 151, 157, 160, 163, 167, 173, 176, 179, 181, 184, 188, 191, 193, 197, 199, 211, 223

Offset: 1

Author

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

Keywords

• nonn

Examples

			45 is in the sequence because 45-phi(45) = 21, which is an octagonal number.
		

Links

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

Crossrefs

Cf. A000010, A000567, A051953.

Cf. A117283, A117284, A117285, A117286, A117287, A117289.

Programs

Mathematica

octQ[n_] := n == 0 || IntegerQ[(Sqrt[48*n + 16] + 4)/12]; Select[Range[250], octQ[# - EulerPhi[#]] &] (* Amiram Eldar, Mar 23 2021 *)

PARI

isok(n) = ispolygonal(n - eulerphi(n), 8); \\ Michel Marcus, Feb 26 2014

Extensions

Offset corrected by Amiram Eldar, Mar 23 2021