A067701 Numbers n such that phi(n-1) + phi(n+1) = phi(2n).

5, 7, 25, 77, 217, 305, 3665, 4645, 5065, 8815, 12205, 12545, 19877, 20435, 24235, 29545, 37735, 47995, 60115, 72085, 73025, 77045, 87475, 121145, 126055, 129245, 149755, 190267, 234635, 247855, 273295, 275723, 419365, 531235, 553475, 621725, 774485, 840085

Offset: 1

Author

Joseph L. Pe, Feb 05 2002

Keywords

• nonn

Examples

			phi(25-1) + phi(25+1) = 8+12 = phi(2*25), so 25 is in the sequence.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000010, A066231.

Programs

Mathematica

Select[Range[10^5], EulerPhi[ # - 1] + EulerPhi[ # + 1] == EulerPhi[2# ] &]
Flatten[Position[Partition[EulerPhi[Range[850000]],3,1],?(#[[1]]+#[[3]]== #[[2]]&),1,Heads->False]]+1 (* _Harvey P. Dale, Mar 26 2023 *)

Extensions

Edited by Dean Hickerson, Feb 12 2002