A117289 Numbers k for which the cototient k-phi(k) is an enneagonal number (A001106).

1, 2, 3, 5, 7, 11, 13, 17, 19, 21, 23, 27, 29, 31, 36, 37, 40, 41, 43, 44, 46, 47, 53, 59, 61, 66, 67, 70, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 207, 211, 219, 223, 227, 229, 231

Offset: 1

Author

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

Keywords

• nonn

Examples

			44 is in the sequence because 44-phi(44) = 24, which is an enneagonal number.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A001106, A051953.

Cf. A117283, A117284, A117285, A117286, A117287, A117288.

Programs

Maple

N:= 1000: # to get all terms <= N
enneagonal:= [seq(n*(7*n-5)/2, n=0..floor((sqrt(25+56*N)+5)/14))]:
select(t -> member(t - numtheory:-phi(t), enneagonal), [$1..N]); # Robert Israel, Mar 30 2018

Mathematica

ennQ[n_] := n == 0 || IntegerQ[(Sqrt[56*n + 25] + 5)/14]; Select[Range[250], ennQ[# - EulerPhi[#]] &] (* Amiram Eldar, Mar 23 2021 *)

PARI

isok(n) = ispolygonal(n - eulerphi(n), 9); \\ Michel Marcus, Feb 26 2014

Extensions

Offset changed to 1 by Robert Israel, Mar 30 2018