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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) = 5.
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%I #30 Sep 25 2024 10:28:29

%S 64,192,288,320,432,448,648,704,729,800,832,960,972,1088,1216,1344,

%T 1440,1458,1472,1568,1856,1984,2000,2016,2112,2160,2240,2368,2400,

%U 2496,2624,2752,3008,3024,3168,3240,3264,3392,3520,3600,3645,3648,3744,3776,3872,3904

%N Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 5.

%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0118439..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024

%H Reinhard Zumkeller, <a href="/A195089/b195089.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)) = 5. - _Reinhard Zumkeller_, Nov 29 2015

%t Select[Range[4000],PrimeOmega[#]-PrimeNu[#]==5&]

%o (PARI) is(n)=bigomega(n)-omega(n)==5 \\ _Charles R Greathouse IV_, Sep 14 2015

%o (Haskell)

%o a195089 n = a195089_list !! (n-1)

%o a195089_list = filter ((== 5) . a046660) [1..]

%o -- _Reinhard Zumkeller_, Nov 29 2015

%Y Cf. A060687, A195069, A195086, A195087, A195088, A195090, 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