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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) = 4.
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%I #34 Sep 25 2024 10:28:34

%S 32,96,144,160,216,224,243,324,352,400,416,480,486,544,608,672,720,

%T 736,784,928,992,1000,1008,1056,1080,1120,1184,1200,1215,1248,1312,

%U 1376,1504,1512,1584,1620,1632,1696,1701,1760,1800,1824,1872,1888,1936,1952

%N Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 4.

%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0237194..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024

%H Reinhard Zumkeller, <a href="/A195088/b195088.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)) = 4. - _Reinhard Zumkeller_, Nov 29 2015

%t Select[Range[2000],PrimeOmega[#]-PrimeNu[#]==4&]

%o (PARI) is(n)=bigomega(n)-omega(n)==4 \\ _Charles R Greathouse IV_, Sep 14 2015

%o (Haskell)

%o a195088 n = a195088_list !! (n-1)

%o a195088_list = filter ((== 4) . a046660) [1..]

%o -- _Reinhard Zumkeller_, Nov 29 2015

%Y Cf. A060687, A195069, A195086, A195087, A195089, 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