A117285 Numbers k for which the cototient k-phi(k) is a pentagonal number.

1, 2, 3, 5, 7, 11, 13, 17, 18, 19, 20, 22, 23, 25, 29, 30, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 75, 79, 83, 89, 97, 101, 102, 103, 107, 109, 110, 113, 127, 131, 132, 137, 139, 140, 149, 151, 155, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 203, 211, 223

Offset: 1

Author

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

Keywords

• nonn

Examples

			30 is in the sequence because 30-phi(30) = 22, which is a pentagonal number.
		

Links

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

Crossrefs

Cf. A000010, A000326, A051953.

Cf. A117283, A117284, A117286, A117287, A117288, A117289.

Programs

Mathematica

pentQ[n_] := n == 0 || IntegerQ[(Sqrt[24*n + 1] + 1)/6]; Select[Range[250], pentQ[# - EulerPhi[#]] &] (* Amiram Eldar, Mar 23 2021 *)

PARI

isok(n) = ispolygonal(n - eulerphi(n), 5); \\ Michel Marcus, Feb 26 2014

Extensions

Offset corrected by Amiram Eldar, Mar 23 2021