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Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 7.
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%I #30 Sep 25 2024 10:28:21

%S 256,768,1152,1280,1728,1792,2592,2816,3200,3328,3840,3888,4352,4864,

%T 5376,5760,5832,5888,6272,6561,7424,7936,8000,8064,8448,8640,8748,

%U 8960,9472,9600,9984,10496,11008,12032,12096,12672,12960,13056,13122,13568

%N Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 7.

%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0029589..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - _Amiram Eldar_, Sep 24 2024

%H Reinhard Zumkeller, <a href="/A195091/b195091.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F A046660(a(n)) = 7. - _Reinhard Zumkeller_, Nov 29 2015

%t Select[Range[14000],PrimeOmega[#]-PrimeNu[#]==7&]

%o (PARI) is(n)=bigomega(n)-omega(n)==7 \\ _Charles R Greathouse IV_, Sep 14 2015

%o (Haskell)

%o a195091 n = a195091_list !! (n-1)

%o a195091_list = filter ((== 7) . a046660) [1..]

%o -- _Reinhard Zumkeller_, Nov 29 2015

%Y Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195092, A195093.

%Y Cf. A025487, A046660, A059956, A112526, A257851, A261256, A264959.

%K nonn,easy

%O 1,1

%A _Harvey P. Dale_, Sep 08 2011