A140707 A positive integer n is included if n written in binary contains the same number of 0's as the number of distinct primes that divide n.

1, 2, 5, 10, 11, 12, 13, 21, 22, 23, 26, 27, 28, 29, 39, 42, 45, 46, 47, 51, 54, 57, 58, 59, 61, 78, 87, 90, 91, 93, 94, 102, 105, 114, 115, 117, 118, 120, 122, 124, 125, 159, 174, 175, 182, 183, 186, 187, 189, 191, 207, 210, 215, 219, 220, 221, 223, 230, 234, 235

Offset: 1

Author

Leroy Quet, Jul 11 2008

Keywords

• base
• nonn

Examples

			90 written in binary is 1011010. There are three 0's in this binary representation. 90 has the prime factorization: 2^1 *3^2 *5^1. There are 3 distinct primes dividing 90. Since the number of 0's in the binary representation equals the number of distinct primes dividing 90, then 90 is in the sequence.
		

Links

• Carl R. White, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071594, A001221, A023416.

Programs

Maple

A080791 := proc(n) local dgs ; dgs := convert(n,base,2) ; nops(dgs)-add(i,i=dgs) ; end: A001221 := proc(n) nops(numtheory[factorset](n)) ; end: isA140707 := proc(n) RETURN( A080791(n) = A001221(n)) ; end: for n from 1 to 300 do if isA140707(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Aug 08 2008

Mathematica

Select[Range[300],DigitCount[#,2,0]==PrimeNu[#]&] (* Harvey P. Dale, Dec 08 2017 *)

Formula

{n: A080791(n) = A001221(n)}. - R. J. Mathar, Aug 08 2008

Extensions

Extended beyond 42 by R. J. Mathar, Aug 08 2008