A053577 Cototient function n - phi(n) is a power of 2.

2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 16, 17, 19, 23, 24, 28, 29, 31, 32, 37, 41, 43, 47, 48, 53, 56, 59, 61, 62, 64, 67, 71, 73, 79, 83, 89, 96, 97, 101, 103, 107, 109, 112, 113, 124, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 192, 193, 197

Offset

1,1

Comments

Consists of all primes, powers of 2, and powers of 2 times Mersenne primes (A000268). - Robert Israel, Jan 29 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

A051953(n) = 2^w.

Example

For p prime, cototient(p)=1; for x in the set {49152,57344,63488,65024,65528,65536}, x-phi(x) = 2^15 = 32768.

Maple

filter:= proc(n) local x; x:= n - numtheory:-phi(n); x = 2^padic:-ordp(x, 2) end proc:
select(filter, [$1..300]); # Robert Israel, Jan 29 2018

Mathematica

Select[Range[200], IntegerQ[Log[2, #-EulerPhi[#]]]&] (* Harvey P. Dale, Dec 14 2011 *)

Prog

(PARI) select(x->hammingweight(x-eulerphi(x))==1, [1..200]) \\ M. F. Hasler, Nov 10 2016

Crossrefs

Cf. A000010, A000268, A051953, A053578.

Sequence in context: A023778 A329299 A173016 * A365127 A093515 A377929

Adjacent sequences: A053574 A053575 A053576 * A053578 A053579 A053580

Keyword

nonn

Author

Labos Elemer, Jan 18 2000

Extensions

Edited by M. F. Hasler, Nov 10 2016

Status

approved