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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) = 3.
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%I #33 Mar 17 2024 02:15:48

%S 16,48,72,80,81,108,112,162,176,200,208,240,272,304,336,360,368,392,

%T 405,464,496,500,504,528,540,560,567,592,600,624,625,656,675,688,752,

%U 756,792,810,816,848,880,891,900,912,936,944,968,976

%N Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 3.

%C The asymptotic density of this sequence is (Sum_{p prime} 1/(p^3*(p+1)) + Sum_{p != q primes} 1/(p^2*(p+1)*q*(q+1)) + Sum_{p < q < r primes} 1/(p*(p+1)*q*(q+1)*r*(r+1)))/zeta(2) = 0.04761... . - _Amiram Eldar_, Sep 03 2022

%H Reinhard Zumkeller, <a href="/A195087/b195087.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 A001222(a(n)) - A001221(a(n)) = 3.

%F A046660(a(n)) = 3. - _Reinhard Zumkeller_, Nov 29 2015

%t Select[Range[1000],PrimeOmega[#]-PrimeNu[#]==3&]

%o (PARI) is(n)=bigomega(n)-omega(n)==3 \\ _Charles R Greathouse IV_, Sep 14 2015

%o (Haskell)

%o a195087 n = a195087_list !! (n-1)

%o a195087_list = filter ((== 3) . a046660) [1..]

%o -- _Reinhard Zumkeller_, Nov 29 2015

%Y Cf. A001221, A001222, A060687, A195069, A195086, A195088, A195089, A195090, A195091, A195092, A195093.

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

%K nonn

%O 1,1

%A _Harvey P. Dale_, Sep 08 2011