A053579 Composite numbers whose cototient (A051953) is a power of 2.

4, 6, 8, 12, 14, 16, 24, 28, 32, 48, 56, 62, 64, 96, 112, 124, 128, 192, 224, 248, 254, 256, 384, 448, 496, 508, 512, 768, 896, 992, 1016, 1024, 1536, 1792, 1984, 2032, 2048, 3072, 3584, 3968, 4064, 4096, 6144, 7168, 7936, 8128, 8192, 12288, 14336

Offset: 1

Author

Labos Elemer, Jan 18 2000

Keywords

• nonn

Examples

			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).
		

Links

• Jud McCranie, Table of n, a(n) for n = 1..316 (First 235 terms from _Donovan Johnson_)

Crossrefs

Cf. A051953.

Programs

Mathematica

Select[Range[4, 15000], And[CompositeQ@ #, IntegerQ@ Log2[# - EulerPhi@ #]] &] (* Michael De Vlieger, Mar 05 2017 *)

PARI

isok(n) = !isprime(n) && (c = (n - eulerphi(n))) && ((c == 2) || (ispower(c, ,&x) && (x == 2))); \\ Michel Marcus, Dec 17 2013