A053163 n+cototient(n) produces these powers of 2 in order of magnitude.

1, 4, 8, 16, 32, 32, 64, 128, 128, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 131072, 262144, 262144, 524288, 524288, 524288, 524288, 1048576, 1048576, 1048576, 2097152

Offset: 1

Author

Labos Elemer, Feb 29 2000

Keywords

• nice
• nonn

Comments

See especially A053579 and also A053576, A053577.

Examples

			1+Mersenne primes powers of 2 are here, 2^p for special primes. Also because of other (infinite) subsequences, all 2-powers from 2^6 occurs at least twice.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..100
• Index to divisibility sequences

Crossrefs

Cf. A000043, A000668, A001348.

Programs

Mathematica

Join[{1}, Reap[For[n=3, n<10^7, n++, If[PrimeNu[k = 2*n - EulerPhi[n]] == 1, Print[k]; Sow[k]]]][[2, 1]]] (* Jean-François Alcover, Jun 30 2015, after Donovan Johnson *)

PARI

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

Formula

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

Extensions

More terms from Olaf Voß, Feb 25 2008