A140707 - OEIS

%I #14 Apr 08 2020 00:09:29

%S 1,2,5,10,11,12,13,21,22,23,26,27,28,29,39,42,45,46,47,51,54,57,58,59,

%T 61,78,87,90,91,93,94,102,105,114,115,117,118,120,122,124,125,159,174,

%U 175,182,183,186,187,189,191,207,210,215,219,220,221,223,230,234,235

%N 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.

%H Carl R. White, <a href="/A140707/b140707.txt">Table of n, a(n) for n = 1..10000</a>

%F {n: A080791(n) = A001221(n)}. - _R. J. Mathar_, Aug 08 2008

%e 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.

%p 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

%t Select[Range[300],DigitCount[#,2,0]==PrimeNu[#]&] (* _Harvey P. Dale_, Dec 08 2017 *)

%Y Cf. A071594, A001221, A023416.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Jul 11 2008

%E Extended beyond 42 by _R. J. Mathar_, Aug 08 2008