A117890 Numbers k such that number of non-leading 0's in binary representation of k divides k.

2, 4, 5, 6, 10, 11, 12, 13, 14, 16, 18, 22, 23, 24, 26, 27, 28, 29, 30, 36, 40, 42, 46, 47, 48, 54, 55, 58, 59, 60, 61, 62, 65, 75, 76, 78, 80, 84, 88, 90, 94, 95, 99, 100, 102, 104, 105, 108, 110, 111, 112, 114, 118, 119, 120, 122, 123, 124, 125, 126, 132, 140, 144, 145

Offset: 1

Author

Leroy Quet, Mar 30 2006

Keywords

• easy
• nonn

Comments

Contains primes of A095078(n) as a subset. Intersection of a(n) with A049445(n) is A117891(n). - R. J. Mathar, Apr 03 2006

Examples

			24 is 11000 in binary. This binary representation has three 0's and 3 divides 24. So 24 is in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A049445, A117891.

Cf. A023416.

Programs

C

#include 
int main(int argc, char *argv[]) { for(int n=1; n< 500; n++) { int digs=0; int nshifted=n; while(nshifted) { digs += 1- nshifted & 1; nshifted >>= 1; } if ( digs) if( n % digs == 0 ) printf("%d, ",n); } } // R. J. Mathar, Apr 03 2006

Haskell

a117890 n = a117890_list !! (n-1)
a117890_list = [x | x <- [1..], let z = a023416 x, z > 0, mod x z == 0]
-- Reinhard Zumkeller, Mar 31 2015

Formula

a(n) <= A117891(n). - R. J. Mathar, Apr 03 2006

a(n) mod A023416(a(n)) = 0. - Reinhard Zumkeller, Nov 22 2007

Extensions

More terms from R. J. Mathar, Apr 03 2006