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A071594 Numbers k such that the number of 1's in the binary representation of k equals omega(k), the number of distinct primes in the factorization of k. 5

%I #18 Jan 11 2020 06:34:10

%S 2,4,6,8,10,12,16,18,20,24,32,33,34,36,40,42,48,64,65,68,70,72,80,84,

%T 96,128,129,136,138,140,144,160,168,192,210,256,266,272,273,276,280,

%U 288,290,320,322,330,336,384,385,390,420,512,513,514,518,522,530,532

%N Numbers k such that the number of 1's in the binary representation of k equals omega(k), the number of distinct primes in the factorization of k.

%H Amiram Eldar, <a href="/A071594/b071594.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2000 from Ivan Neretin)

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

%t Select[Range[2, 1000], Length[FactorInteger[#]] == DigitCount[#, 2, 1] &] (* _Ivan Neretin_, May 30 2015 *)

%o (PARI) for(n=1,1000,if(sum(i=1,length(binary(n)), component(binary(n),i))==omega(n),print1(n,",")))

%o (PARI) select(n->hammingweight(n)==omega(n), vector(1000, n, n)) \\ _Michel Marcus_, May 30 2015

%Y Cf. A071595, A071596, A071814.

%K base,easy,nonn

%O 1,1

%A _Benoit Cloitre_, Jun 01 2002

%E Name edited by _Amiram Eldar_, Jan 11 2020

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)