A195093 - OEIS

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A195093

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

1024, 3072, 4608, 5120, 6912, 7168, 10368, 11264, 12800, 13312, 15360, 15552, 17408, 19456, 21504, 23040, 23328, 23552, 25088, 29696, 31744, 32000, 32256, 33792, 34560, 34992, 35840, 37888, 38400, 39936, 41984, 44032, 48128, 48384

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OFFSET

1,1

COMMENTS

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

FORMULA

A046660(a(n)) = 9. - Reinhard Zumkeller, Nov 29 2015

MATHEMATICA

Select[Range[50000], PrimeOmega[#]-PrimeNu[#]==9&]

PROG

(PARI) is(n)=bigomega(n)-omega(n)==9 \\ Charles R Greathouse IV, Sep 14 2015

(Haskell)

a195093 n = a195093_list !! (n-1)

a195093_list = filter ((== 9) . a046660) [1..]