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Numbers k such that the number of 1's in the binary representation of k equals bigomega(k), the number of prime divisors of k (counted with multiplicity).
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%I #21 Apr 13 2024 14:56:30

%S 2,6,9,10,28,33,34,42,44,50,52,54,60,65,70,76,90,98,129,135,138,148,

%T 150,156,164,184,198,204,210,225,228,232,261,266,268,273,290,292,294,

%U 297,306,308,322,330,340,344,385,388,390,405,424,440,468,486,496,504

%N Numbers k such that the number of 1's in the binary representation of k equals bigomega(k), the number of prime divisors of k (counted with multiplicity).

%C A115156 is a subsequence: A001222(A115156(n)) = A000120(A115156(n)) = n. - _Reinhard Zumkeller_, Jan 14 2006

%H Ivan Neretin, <a href="/A071814/b071814.txt">Table of n, a(n) for n = 1..10000</a>

%e 232 is a term because 232 = 11101000_2 and 232 = 2^3*29.

%t fQ[n_] := Count[IntegerDigits[n, 2], 1] == Plus @@ Last /@ FactorInteger@n; Select[ Range@517, fQ[ # ] &] (* _Robert G. Wilson v_, Jan 18 2006 *)

%t Select[Range[600],Count[IntegerDigits[#,2],1]==PrimeOmega[#]&] (* _Harvey P. Dale_, Mar 07 2019 *)

%Y Cf. A000120, A001222, A071594, A115156.

%K easy,nonn

%O 1,1

%A _Jason Earls_, Jun 07 2002