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A053577 Cototient function n - phi(n) is a power of 2. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A032847 A023778 A173016 * A093515 A249724 A084369

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

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)