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.

Equivalently, numbers all of whose divisors > 1 are evil (A001969). - Bernard Schott, Jul 24 2022

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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

(PARI) is(n)=sumdiv(n, d, hammingweight(d)%2)==1 \\ Charles R Greathouse IV, Mar 28 2013

(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))

print([k for k in range(480) if ok(k)]) # Michael S. Branicky, Jul 24 2022

CROSSREFS

KEYWORD

nonn,base,easy

AUTHOR

Jason Earls, May 16 2004

EXTENSIONS

a(1) added by Charles R Greathouse IV, Mar 28 2013

STATUS

approved