cp's OEIS Frontend

A195092 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 8.

%I A195092 #30 Sep 25 2024 10:28:17
%S A195092 512,1536,2304,2560,3456,3584,5184,5632,6400,6656,7680,7776,8704,9728,
%T A195092 10752,11520,11664,11776,12544,14848,15872,16000,16128,16896,17280,
%U A195092 17496,17920,18944,19200,19683,19968,20992,22016,24064,24192
%N A195092 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 8.
%C A195092 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 A195092 Reinhard Zumkeller, <a href="/A195092/b195092.txt">Table of n, a(n) for n = 1..10000</a>
%H A195092 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A195092 A046660(a(n)) = 8. - _Reinhard Zumkeller_, Nov 29 2015
%t A195092 Select[Range[25000],PrimeOmega[#]-PrimeNu[#]==8&]
%o A195092 (PARI) is(n)=bigomega(n)-omega(n)==8 \\ _Charles R Greathouse IV_, Sep 14 2015
%o A195092 (Haskell)
%o A195092 a195092 n = a195092_list !! (n-1)
%o A195092 a195092_list = filter ((== 8) . a046660) [1..]
%o A195092 -- _Reinhard Zumkeller_, Nov 29 2015
%Y A195092 Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195091, A195093.
%Y A195092 Cf. A025487, A046660, A059956, A112526, A257851, A261256, A264959.
%K A195092 nonn,easy
%O A195092 1,1
%A A195092 _Harvey P. Dale_, Sep 08 2011