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
Keywords
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
Programs
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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
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Mathematica
ennQ[n_] := n == 0 || IntegerQ[(Sqrt[56*n + 25] + 5)/14]; Select[Range[250], ennQ[# - EulerPhi[#]] &] (* Amiram Eldar, Mar 23 2021 *)
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PARI
isok(n) = ispolygonal(n - eulerphi(n), 9); \\ Michel Marcus, Feb 26 2014
Extensions
Offset changed to 1 by Robert Israel, Mar 30 2018