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A053577 Cototient function n - phi(n) is a power of 2. 5

%I

%S 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,

%T 53,56,59,61,62,64,67,71,73,79,83,89,96,97,101,103,107,109,112,113,

%U 124,127,128,131,137,139,149,151,157,163,167,173,179,181,191,192,193,197

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

%C Consists of all primes, powers of 2, and powers of 2 times Mersenne primes (A000268). - _Robert Israel_, Jan 29 2018

%H Robert Israel, <a href="/A053577/b053577.txt">Table of n, a(n) for n = 1..10000</a>

%F A051953(n) = 2^w.

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

%p filter:= proc(n) local x; x:= n - numtheory:-phi(n); x = 2^padic:-ordp(x,2) end proc:

%p select(filter, [$1..300]); # _Robert Israel_, Jan 29 2018

%t Select[Range[200],IntegerQ[Log[2,#-EulerPhi[#]]]&] (* _Harvey P. Dale_, Dec 14 2011 *)

%o (PARI) select(x->hammingweight(x-eulerphi(x))==1,[1..200]) \\ _M. F. Hasler_, Nov 10 2016

%Y Cf. A000010, A000268, A051953, A053578.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 18 2000

%E Edited by _M. F. Hasler_, Nov 10 2016

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Last modified August 14 01:48 EDT 2020. Contains 336474 sequences. (Running on oeis4.)