

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



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
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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 0s 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 0s 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



