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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) = 9.
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%I #30 Sep 25 2024 10:28:12

%S 1024,3072,4608,5120,6912,7168,10368,11264,12800,13312,15360,15552,

%T 17408,19456,21504,23040,23328,23552,25088,29696,31744,32000,32256,

%U 33792,34560,34992,35840,37888,38400,39936,41984,44032,48128,48384

%N Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9.

%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0007396..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024

%H Reinhard Zumkeller, <a href="/A195093/b195093.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)) = 9. - _Reinhard Zumkeller_, Nov 29 2015

%t Select[Range[50000],PrimeOmega[#]-PrimeNu[#]==9&]

%o (PARI) is(n)=bigomega(n)-omega(n)==9 \\ _Charles R Greathouse IV_, Sep 14 2015

%o (Haskell)

%o a195093 n = a195093_list !! (n-1)

%o a195093_list = filter ((== 9) . a046660) [1..]

%o -- _Reinhard Zumkeller_, Nov 29 2015

%Y Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195091, A195092.

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

%K nonn,easy

%O 1,1

%A _Harvey P. Dale_, Sep 08 2011