A053159 Numbers n such that n+cototient(n) is a power of 2.

1, 3, 7, 10, 20, 31, 40, 80, 127, 160, 320, 322, 640, 644, 1280, 1288, 2560, 2576, 5120, 5152, 8191, 10240, 10304, 20480, 20608, 40960, 41216, 81920, 82432, 131071, 163840, 164864, 327680, 329728, 333634, 524287, 655360, 659456, 667268, 1310720, 1318912

Offset: 1

Author

Labos Elemer, Feb 29 2000

Keywords

• nonn

Comments

See especially A053579 and also A053576, A053577.

Examples

			Mersenne primes are a proper subset of this sequence: A(M)=2M-M+1=M+1=2^p
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000043, A000668, A001348.

Programs

PARI

print(1); for(n=3, 10^9, if(omega(2*n-eulerphi(n))==1, print(n))) /* Donovan Johnson, Apr 04 2013 */

Formula

a(n)+A051953(n) = 2*a(n)-A000010(n) = 2^w for some w.

Extensions

More terms from Reiner Martin, Dec 24 2001