cp's OEIS Frontend

A195090 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 6.

%I A195090 #28 Sep 25 2024 10:28:25
%S A195090 128,384,576,640,864,896,1296,1408,1600,1664,1920,1944,2176,2187,2432,
%T A195090 2688,2880,2916,2944,3136,3712,3968,4000,4032,4224,4320,4374,4480,
%U A195090 4736,4800,4992,5248,5504,6016,6048,6336,6480,6528,6784
%N A195090 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 6.
%C A195090 The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0059189..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024
%H A195090 Reinhard Zumkeller, <a href="/A195090/b195090.txt">Table of n, a(n) for n = 1..10000</a>
%H A195090 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A195090 A046660(a(n)) = 6. - _Reinhard Zumkeller_, Nov 29 2015
%p A195090 op(select(n->bigomega(n)-nops(factorset(n))=6, [$1..6784])); # _Paolo P. Lava_, Jul 03 2018
%t A195090 Select[Range[7000],PrimeOmega[#]-PrimeNu[#]==6&]
%o A195090 (PARI) is(n)=bigomega(n)-omega(n)==6 \\ _Charles R Greathouse IV_, Sep 14 2015
%o A195090 (Haskell)
%o A195090 a195090 n = a195090_list !! (n-1)
%o A195090 a195090_list = filter ((== 6) . a046660) [1..]
%o A195090 -- _Reinhard Zumkeller_, Nov 29 2015
%Y A195090 Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195091, A195092, A195093.
%Y A195090 Cf. A025487, A046660, A059956, A112526, A257851, A261256, A264959.
%K A195090 nonn,easy
%O A195090 1,1
%A A195090 _Harvey P. Dale_, Sep 08 2011