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

1,1

Links

Jud McCranie, Table of n, a(n) for n = 1..316 (First 235 terms from Donovan Johnson)

Example

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A051953.

Sequence in context: A107303 A028876 A271346 * A074121 A175088 A275671

Adjacent sequences: A053576 A053577 A053578 * A053580 A053581 A053582

Keyword

nonn

Author

Labos Elemer, Jan 18 2000

Status

approved