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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) = 8.
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%I #30 Sep 25 2024 10:28:17

%S 512,1536,2304,2560,3456,3584,5184,5632,6400,6656,7680,7776,8704,9728,

%T 10752,11520,11664,11776,12544,14848,15872,16000,16128,16896,17280,

%U 17496,17920,18944,19200,19683,19968,20992,22016,24064,24192

%N Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 8.

%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0014793..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024

%H Reinhard Zumkeller, <a href="/A195092/b195092.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)) = 8. - _Reinhard Zumkeller_, Nov 29 2015

%t Select[Range[25000],PrimeOmega[#]-PrimeNu[#]==8&]

%o (PARI) is(n)=bigomega(n)-omega(n)==8 \\ _Charles R Greathouse IV_, Sep 14 2015

%o (Haskell)

%o a195092 n = a195092_list !! (n-1)

%o a195092_list = filter ((== 8) . a046660) [1..]

%o -- _Reinhard Zumkeller_, Nov 29 2015

%Y Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195091, A195093.

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

%K nonn,easy

%O 1,1

%A _Harvey P. Dale_, Sep 08 2011