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A117286
Numbers k for which the cototient k-phi(k) is a hexagonal number.
7
1, 2, 3, 5, 7, 10, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 47, 52, 53, 55, 59, 61, 67, 71, 73, 79, 83, 89, 90, 97, 101, 103, 107, 109, 113, 117, 127, 129, 131, 137, 139, 149, 151, 157, 163, 167, 168, 173, 179, 181, 191, 193, 197, 199, 200, 205, 211, 223, 227, 229
OFFSET
1,2
COMMENTS
55 is in the sequence because 55-phi(55) = 15, which is a hexagonal number.
LINKS
MATHEMATICA
cthQ[n_]:=Module[{c=n-EulerPhi[n]}, IntegerQ[(Sqrt[1+8c]+1)/4]]; Join[{1}, Select[Range[250], cthQ]] (* Harvey P. Dale, Jan 16 2012 *)
PROG
(PARI) isok(n) = ispolygonal(n - eulerphi(n), 6); \\ Michel Marcus, Feb 26 2014
KEYWORD
nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006
EXTENSIONS
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved