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%I #25 Jul 05 2022 23:30:18
%S 1,2,12,20,28,36,44,52,68,76,92,100,108,116,120,124,148,164,168,172,
%T 188,196,212,236,244,264,268,280,284,292,312,316,324,332,356,360,388,
%U 404,408,412,428,436,440,452,456,484,500,504,508,520,524,548,552,556
%N Numbers n such that the largest power of 2 dividing n equals 2^omega(n).
%C That is, numbers such that A001221(n) is equal to A007814(n).
%C omega(n) = A001221(n) is the number of distinct primes dividing n.
%C And A007814(n) is the exponent of the highest power of 2 dividing n.
%H G. C. Greubel, <a href="/A023534/b023534.txt">Table of n, a(n) for n = 1..1000</a>
%e omega(12)=2 and 4=2^2 is the largest power of 2 dividing 12, hence 12 is in the sequence.
%t Select[Range[600],IntegerExponent[#,2]==PrimeNu[#]&] (* _Harvey P. Dale_, Jun 26 2011 *)
%o (PARI) isok(n) = omega(n) == valuation(n, 2); \\ _Michel Marcus_, Apr 16 2015
%o (Python)
%o from itertools import count, islice
%o from sympy.ntheory.factor_ import primenu
%o def A023534_gen(startvalue=1): # generator of terms
%o return filter(lambda n:(~n & n-1).bit_length() == primenu(n),count(max(startvalue,1)))
%o A023534_list = list(islice(A023534_gen(),30)) # _Chai Wah Wu_, Jul 05 2022
%Y Cf. A039700, A001221 (omega), A007814 (2-adic valuation).
%K nonn
%O 1,2
%A _Benoit Cloitre_, Sep 04 2002
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