A053162 Nonprimes n such that n+cototient(n) is a power of 2.

1, 10, 20, 40, 80, 160, 320, 322, 640, 644, 1280, 1288, 2560, 2576, 5120, 5152, 10240, 10304, 20480, 20608, 40960, 41216, 81920, 82432, 163840, 164864, 327680, 329728, 333634, 655360, 659456, 667268, 1310720, 1318912, 1334536, 1378114, 2621440

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 and a(n).

Example

Mersenne primes were deleted from set of numbers with similar property. An infinite subset here is m(r)=5*2^r, since Phi[m(r)]=2^(r+1) and a(m(r))=5*2^(r+1)-2^(r+1)=2^(r+3). A different subset includes m = 322,644,1288,.. = Set of {(2^s)*7*23} generating 2^(s+8)=2m-Phi(m) powers of 2.

Prog

(PARI) for(n=1, 2621440, if(isprime(n)==0, if(omega((2*n-eulerphi(n))*2)==1, print1(n ", ")))) \\ Donovan Johnson, Jan 09 2014

Crossrefs

Cf. A000043, A000668, A001348, A053159.

Sequence in context: A114931 A013978 A241608 * A110804 A048063 A007927

Adjacent sequences: A053159 A053160 A053161 * A053163 A053164 A053165

Keyword

nonn

Author

Labos Elemer, Feb 29 2000

Extensions

More terms from Olaf Voß, Feb 25 2008

Status

approved