|
|
A093688
|
|
Numbers m such that all divisors of m, excluding the divisor 1, have an even number of 1's in their binary expansions.
|
|
10
|
|
|
1, 3, 5, 9, 15, 17, 23, 27, 29, 43, 45, 51, 53, 71, 83, 85, 89, 101, 113, 129, 135, 139, 149, 153, 159, 163, 197, 215, 249, 255, 257, 263, 267, 269, 277, 281, 293, 303, 311, 317, 337, 347, 349, 353, 359, 373, 383, 387, 389, 401, 417, 447, 449, 459, 461, 467, 479
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Putting the 1 aside, these could be called odiousfree numbers, and are a subsequence of A001969. A093696 would be the evilfree numbers then. - Irina Gerasimova, Feb 08 2014.
|
|
LINKS
|
|
|
EXAMPLE
|
51 is in the sequence because, excluding 1, its divisors are 3, 17 and 51.
In binary: 11, 10001, 110011 all have an even number of 1's.
|
|
MATHEMATICA
|
okQ[n_] := AllTrue[Rest[Divisors[n]], EvenQ[Total[IntegerDigits[#, 2]]]&]; Select[Range[500], okQ] (* Jean-François Alcover, Dec 06 2015 *)
|
|
PROG
|
(Python)
from sympy import divisors
def c(n): return n == 1 or bin(n).count("1")&1 == 0
def ok(n): return n > 0 and all(c(d) for d in divisors(n, generator=True))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|