cp's OEIS Frontend

A195093 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9.

%I A195093 #30 Sep 25 2024 10:28:12
%S A195093 1024,3072,4608,5120,6912,7168,10368,11264,12800,13312,15360,15552,
%T A195093 17408,19456,21504,23040,23328,23552,25088,29696,31744,32000,32256,
%U A195093 33792,34560,34992,35840,37888,38400,39936,41984,44032,48128,48384
%N A195093 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9.
%C A195093 The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0007396..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024
%H A195093 Reinhard Zumkeller, <a href="/A195093/b195093.txt">Table of n, a(n) for n = 1..10000</a>
%H A195093 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A195093 A046660(a(n)) = 9. - _Reinhard Zumkeller_, Nov 29 2015
%t A195093 Select[Range[50000],PrimeOmega[#]-PrimeNu[#]==9&]
%o A195093 (PARI) is(n)=bigomega(n)-omega(n)==9 \\ _Charles R Greathouse IV_, Sep 14 2015
%o A195093 (Haskell)
%o A195093 a195093 n = a195093_list !! (n-1)
%o A195093 a195093_list = filter ((== 9) . a046660) [1..]
%o A195093 -- _Reinhard Zumkeller_, Nov 29 2015
%Y A195093 Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195091, A195092.
%Y A195093 Cf. A025487, A046660, A059956, A112526, A257851, A261256, A264959.
%K A195093 nonn,easy
%O A195093 1,1
%A A195093 _Harvey P. Dale_, Sep 08 2011