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

1,2

Comments

See especially A053579 and also A053576, A053577.

Links

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

Formula

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

Example

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

Prog

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

Crossrefs

Cf. A000043, A000668, A001348.

Sequence in context: A366044 A031328 A255180 * A345891 A279912 A305477

Adjacent sequences: A053156 A053157 A053158 * A053160 A053161 A053162

Keyword

nonn

Author

Labos Elemer, Feb 29 2000

Extensions

More terms from Reiner Martin, Dec 24 2001

Status

approved