A064548 Numbers k for which the sum of the binary digits equals the number of prime factors of k + 1 counted with multiplicity.

1, 2, 3, 4, 5, 7, 9, 11, 15, 16, 19, 20, 23, 24, 26, 31, 33, 34, 39, 41, 44, 47, 48, 49, 53, 63, 67, 68, 69, 74, 79, 83, 89, 95, 97, 98, 99, 104, 107, 127, 132, 135, 137, 139, 144, 146, 149, 152, 159, 160, 164, 167, 179, 191, 194, 195, 197, 199, 209, 215, 242, 255

Offset: 1

Author

Wouter Meeussen, Oct 09 2001

Keywords

• nonn

Comments

This sequence becomes rare for large n: 15 values between 100000 and 101024 and none between 1000000 and 1001024.

Numbers k such that A000120(k) = A001222(k+1). - Franklin T. Adams-Watters, Aug 17 2012

Examples

			8 is absent since 8 in binary is (1000) with sum=1, while (8+1) has 2 factors.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000120, A001222, A058061, A064547.

Programs

Mathematica

Select[ Range[ 1024 ], DigitCount[ #, 2, 1 ]===(Plus@@(Last/@FactorInteger[ #+1 ]))& ]
Select[Range[300],DigitCount[#,2,1]==PrimeOmega[#+1]&] (* Harvey P. Dale, Mar 11 2023 *)

PARI

isok(k) = { hammingweight(k) == bigomega(k+1) } \\ Harry J. Smith, Sep 18 2009