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A117289
Numbers k for which the cototient k-phi(k) is an enneagonal number (A001106).
7
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
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
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