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

1,2

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A071594, A001221, A023416.

Sequence in context: A182179 A123466 A144793 * A257086 A136817 A140180

Adjacent sequences: A140704 A140705 A140706 * A140708 A140709 A140710

Keyword

base,nonn

Author

Leroy Quet, Jul 11 2008

Extensions

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

Status

approved