A053577 Cototient function n - phi(n) is a power of 2.

2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 16, 17, 19, 23, 24, 28, 29, 31, 32, 37, 41, 43, 47, 48, 53, 56, 59, 61, 62, 64, 67, 71, 73, 79, 83, 89, 96, 97, 101, 103, 107, 109, 112, 113, 124, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 192, 193, 197

Offset: 1

Author

Labos Elemer, Jan 18 2000

Keywords

• nonn

Comments

Consists of all primes, powers of 2, and powers of 2 times Mersenne primes (A000268). - Robert Israel, Jan 29 2018

Examples

			For p prime, cototient(p)=1; for x in the set {49152,57344,63488,65024,65528,65536}, x-phi(x) = 2^15 = 32768.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000268, A051953, A053578.

Programs

Maple

filter:= proc(n) local x; x:= n - numtheory:-phi(n); x = 2^padic:-ordp(x,2) end proc:
select(filter, [$1..300]); # Robert Israel, Jan 29 2018

Mathematica

Select[Range[200],IntegerQ[Log[2,#-EulerPhi[#]]]&] (* Harvey P. Dale, Dec 14 2011 *)

PARI

select(x->hammingweight(x-eulerphi(x))==1,[1..200]) \\ M. F. Hasler, Nov 10 2016

Formula

A051953(n) = 2^w.

Extensions

Edited by M. F. Hasler, Nov 10 2016