A050472 Numbers m such that 2*phi(m) = phi(m+1).

2, 4, 16, 154, 256, 286, 364, 804, 1066, 2146, 3382, 4550, 6106, 7700, 8176, 9268, 11284, 12556, 12970, 16402, 19228, 19276, 20272, 25132, 26404, 27346, 29154, 29574, 35644, 36418, 38368, 39646, 40494, 47214, 52234, 54652, 65536, 84862

Offset: 1

Author

Jud McCranie, Dec 24 1999

Keywords

• nonn

Examples

			phi(256)=128, phi(256+1)=2*128, so 256 is a member of the sequence.
		

References

• R. K. Guy, Unsolved Problems Number Theory, Sect. B36.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Donovan Johnson)

Crossrefs

Cf. A000010, A001274, A050473, A171271.

Programs

Mathematica

Select[Range[85000], 2EulerPhi[#]==EulerPhi[#+1] &] (* Stefano Spezia, Apr 07 2025 *)

PARI

isok(n) = 2*eulerphi(n) == eulerphi(n+1); \\ Michel Marcus, Aug 02 2018

Formula

Conjecture : a(n)/n^3 is bounded. Does lim n -> infinity a(n)/n^3 = 2 ? - Benoit Cloitre, Aug 07 2002

a(n) = A171271(n) - 1. - Ray Chandler, May 01 2015