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%I #19 Jul 13 2017 22:25:40
%S 4,6,8,12,14,16,24,28,32,48,56,62,64,96,112,124,128,192,224,248,254,
%T 256,384,448,496,508,512,768,896,992,1016,1024,1536,1792,1984,2032,
%U 2048,3072,3584,3968,4064,4096,6144,7168,7936,8128,8192,12288,14336
%N Composite numbers whose cototient (A051953) is a power of 2.
%H Jud McCranie, <a href="/A053579/b053579.txt">Table of n, a(n) for n = 1..316</a> (First 235 terms from _Donovan Johnson_)
%e If n = 3*2^s, cototient(n) = 3*2^s-2*2^(s-1)=2^(s+1); if n = 7*2^s, cototient(n) = (7-6)*2^(s-1) = 2^(s+2). If cototient(x) = 32768, then arguments are 3*16384, 7*8192, 31*2048, 127*512, 8191*8 and 65536. If n = (2^w)*q, where q is a Mersenne prime, then phi(n) = (q-1)*2^(w-1) and the cototient(n) = 2^(w-1)*(2q-q+1) = 2^(w-1)*(q+1) = 2^(w-1+s).
%t Select[Range[4, 15000], And[CompositeQ@ #, IntegerQ@ Log2[# - EulerPhi@ #]] &] (* _Michael De Vlieger_, Mar 05 2017 *)
%o (PARI) isok(n) = !isprime(n) && (c = (n - eulerphi(n))) && ((c == 2) || (ispower(c, ,&x) && (x == 2))); \\ _Michel Marcus_, Dec 17 2013
%Y Cf. A051953.
%K nonn
%O 1,1
%A _Labos Elemer_, Jan 18 2000
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