login
A117285
Numbers k for which the cototient k-phi(k) is a pentagonal number.
7
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
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
KEYWORD
nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006
EXTENSIONS
Offset corrected by Amiram Eldar, Mar 23 2021
STATUS
approved