cp's OEIS Frontend

A195087 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 3.

%I A195087 #33 Mar 17 2024 02:15:48
%S A195087 16,48,72,80,81,108,112,162,176,200,208,240,272,304,336,360,368,392,
%T A195087 405,464,496,500,504,528,540,560,567,592,600,624,625,656,675,688,752,
%U A195087 756,792,810,816,848,880,891,900,912,936,944,968,976
%N A195087 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 3.
%C A195087 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 A195087 Reinhard Zumkeller, <a href="/A195087/b195087.txt">Table of n, a(n) for n = 1..10000</a>
%H A195087 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A195087 A001222(a(n)) - A001221(a(n)) = 3.
%F A195087 A046660(a(n)) = 3. - _Reinhard Zumkeller_, Nov 29 2015
%t A195087 Select[Range[1000],PrimeOmega[#]-PrimeNu[#]==3&]
%o A195087 (PARI) is(n)=bigomega(n)-omega(n)==3 \\ _Charles R Greathouse IV_, Sep 14 2015
%o A195087 (Haskell)
%o A195087 a195087 n = a195087_list !! (n-1)
%o A195087 a195087_list = filter ((== 3) . a046660) [1..]
%o A195087 -- _Reinhard Zumkeller_, Nov 29 2015
%Y A195087 Cf. A001221, A001222, A060687, A195069, A195086, A195088, A195089, A195090, A195091, A195092, A195093.
%Y A195087 Cf. A025487, A046660, A257851, A261256, A264959.
%K A195087 nonn
%O A195087 1,1
%A A195087 _Harvey P. Dale_, Sep 08 2011