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A053579 Composite numbers whose cototient (A051953) is a power of 2. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 11 06:10 EDT 2020. Contains 336422 sequences. (Running on oeis4.)