cp's OEIS Frontend

A195069 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 10.

%I A195069 #31 Sep 25 2024 10:28:38
%S A195069 2048,6144,9216,10240,13824,14336,20736,22528,25600,26624,30720,31104,
%T A195069 34816,38912,43008,46080,46656,47104,50176,59392,63488,64000,64512,
%U A195069 67584,69120,69984,71680,75776,76800,79872,83968,88064,96256,96768,101376,103680,104448
%N A195069 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 10.
%C A195069 The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0003698..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 25 2024
%H A195069 Reinhard Zumkeller, <a href="/A195069/b195069.txt">Table of n, a(n) for n = 1..10000</a>
%H A195069 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A195069 A046660(a(n)) = 10. - _Reinhard Zumkeller_, Nov 29 2015
%e A195069 14336 = 2^11 * 7^1, so it has 12 prime factors (counted with multiplicity) and 2 distinct prime factors, and 12-2 = 10.
%p A195069 op(select(n->bigomega(n)-nops(factorset(n))=10, [$1..104448])); # _Paolo P. Lava_, Jul 03 2018
%t A195069 Select[Range[200000], PrimeOmega[#] - PrimeNu[#] == 10&]
%o A195069 (Haskell)
%o A195069 a195069 n = a195069_list !! (n-1)
%o A195069 a195069_list = filter ((== 10) . a046660) [1..]
%o A195069 -- _Reinhard Zumkeller_, Nov 29 2015
%o A195069 (PARI) isok(n) = bigomega(n) - omega(n) == 10; \\ _Michel Marcus_, Jul 03 2018
%Y A195069 Cf. A025487, A060687, A195087, A195088, A195089, A195090, A195091, A195092, A195093.
%Y A195069 Cf. A046660, A059956, A112526, A257851, A261256, A264959.
%K A195069 nonn,easy
%O A195069 1,1
%A A195069 _Harvey P. Dale_, Sep 08 2011