A195089 - OEIS

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A195089

Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 5.

64, 192, 288, 320, 432, 448, 648, 704, 729, 800, 832, 960, 972, 1088, 1216, 1344, 1440, 1458, 1472, 1568, 1856, 1984, 2000, 2016, 2112, 2160, 2240, 2368, 2400, 2496, 2624, 2752, 3008, 3024, 3168, 3240, 3264, 3392, 3520, 3600, 3645, 3648, 3744, 3776, 3872, 3904

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OFFSET

1,1

COMMENTS

The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0118439..., 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)) = 5. - Reinhard Zumkeller, Nov 29 2015

MATHEMATICA

Select[Range[4000], PrimeOmega[#]-PrimeNu[#]==5&]

PROG

(PARI) is(n)=bigomega(n)-omega(n)==5 \\ Charles R Greathouse IV, Sep 14 2015

(Haskell)

a195089 n = a195089_list !! (n-1)

a195089_list = filter ((== 5) . a046660) [1..]