A161152 Positive integers n such that {the number of (non-leading) 0's in the binary representation of n} is coprime to n.

1, 2, 5, 6, 8, 9, 11, 13, 14, 17, 19, 20, 21, 23, 25, 27, 29, 30, 32, 33, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 52, 53, 55, 56, 57, 59, 61, 62, 66, 67, 68, 69, 71, 72, 73, 77, 79, 81, 83, 85, 86, 87, 89, 91, 92, 93, 95, 96, 97, 101, 103, 106, 107, 109, 111, 113, 115

Offset: 1

Author

Leroy Quet, Jun 03 2009

Keywords

• base
• nonn

Comments

1 is the only integer of the form 2^k - 1 (k>=0) included in this sequence, because such integers contain no binary 0's, and 0 is considered here to be coprime only to 1.

Examples

			13 is in the sequence because the number of non-leading 0 s in the binary representation of 13 is 1 (13_10 = 1101_2) and gcd(1, 13) = 1. - _Indranil Ghosh_, Mar 08 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A023416, A094387, A161153, A161154, A161155, A161156.

Programs

Mathematica

Select[Range[115], GCD[DigitCount[#, 2, 0], #] == 1 &] (* Indranil Ghosh, Mar 08 2017 *)

PARI

b(n) = if(n<1, 0, b(n\2) + 1 - n%2);
for (n=1, 115, if(gcd(b(n),n)==1, print1(n", "))); \\ Indranil Ghosh, Mar 08 2017

Python

from math import gcd
i=j=1
while j<=100:
    if gcd(bin(i)[2:].count("0"),i)==1:
        print(j, i)
        j+=1
    i+=1 # Indranil Ghosh, Mar 08 2017

Extensions

Extended by Ray Chandler, Jun 11 2009