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

1,2

Comments

See especially A053579 and also A053576, A053577.

Links

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

Index to divisibility sequences

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000043, A000668, A001348.

Sequence in context: A320947 A329778 A355391 * A125626 A141031 A061011

Adjacent sequences: A053160 A053161 A053162 * A053164 A053165 A053166

Keyword

nice,nonn

Author

Labos Elemer, Feb 29 2000

Extensions

More terms from Olaf Voß, Feb 25 2008

Status

approved