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

1,1

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A071594, A071596.

Sequence in context: A163411 A335669 A339908 * A225707 A225511 A248038

Adjacent sequences: A071592 A071593 A071594 * A071596 A071597 A071598

Keyword

base,easy,nonn

Author

Benoit Cloitre, Jun 01 2002

Status

approved