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Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 6.
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%I #28 Sep 25 2024 10:28:25

%S 128,384,576,640,864,896,1296,1408,1600,1664,1920,1944,2176,2187,2432,

%T 2688,2880,2916,2944,3136,3712,3968,4000,4032,4224,4320,4374,4480,

%U 4736,4800,4992,5248,5504,6016,6048,6336,6480,6528,6784

%N Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 6.

%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0059189..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024

%H Reinhard Zumkeller, <a href="/A195090/b195090.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F A046660(a(n)) = 6. - _Reinhard Zumkeller_, Nov 29 2015

%p op(select(n->bigomega(n)-nops(factorset(n))=6, [$1..6784])); # _Paolo P. Lava_, Jul 03 2018

%t Select[Range[7000],PrimeOmega[#]-PrimeNu[#]==6&]

%o (PARI) is(n)=bigomega(n)-omega(n)==6 \\ _Charles R Greathouse IV_, Sep 14 2015

%o (Haskell)

%o a195090 n = a195090_list !! (n-1)

%o a195090_list = filter ((== 6) . a046660) [1..]

%o -- _Reinhard Zumkeller_, Nov 29 2015

%Y Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195091, A195092, A195093.

%Y Cf. A025487, A046660, A059956, A112526, A257851, A261256, A264959.

%K nonn,easy

%O 1,1

%A _Harvey P. Dale_, Sep 08 2011