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

1,2

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000010, A001106, A051953.

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

Sequence in context: A331046 A329150 A230606 * A339817 A328513 A318719

Adjacent sequences: A117286 A117287 A117288 * A117290 A117291 A117292

Keyword

nonn

Author

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

Extensions

Offset changed to 1 by Robert Israel, Mar 30 2018

Status

approved