A071595 Odd numbers k such that the number of 1's in binary representation of k equals omega(k), the number of distinct primes in the factorization of k.

33, 65, 129, 273, 385, 513, 1025, 1155, 1281, 2049, 2065, 2145, 4097, 4161, 4641, 8193, 8195, 8211, 8225, 8265, 8385, 8449, 9345, 10241, 16905, 17409, 21505, 24585, 32775, 32785, 32835, 32865, 33033, 33285, 33345, 33825, 34881, 36865, 36993

Offset: 1

Author

Benoit Cloitre, Jun 01 2002

Keywords

• base
• easy
• nonn

Examples

			129 = 10000001 in base 2 and 129 = 3*43 hence 129 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A071594, A071596.

Programs

Mathematica

Select[Range[1, 37000, 2], DigitCount[#, 2, 1] == PrimeNu[#] &] (* Amiram Eldar, Jan 11 2020*)

PARI

for(n=1,80000,if(sum(i=1,length(binary(n)), component(binary(n),i))==-(-1)^n*omega(n),print1(n,",")))