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

1,2

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000120, A001222, A058061, A064547.

Sequence in context: A111133 A279076 A076970 * A291927 A239497 A039850

Adjacent sequences: A064545 A064546 A064547 * A064549 A064550 A064551

Keyword

nonn

Author

Wouter Meeussen, Oct 09 2001

Status

approved