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

1,2

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A000326, A051953.

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

Sequence in context: A171049 A171053 A171055 * A100546 A359373 A117094

Adjacent sequences: A117282 A117283 A117284 * A117286 A117287 A117288

Keyword

nonn

Author

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

Extensions

Offset corrected by Amiram Eldar, Mar 23 2021

Status

approved