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

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..]
-- Reinhard Zumkeller, Nov 29 2015

Crossrefs

Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195091, A195092.

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

Sequence in context: A223065 A298607 A366391 * A258734 A195234 A257650

Adjacent sequences: A195090 A195091 A195092 * A195094 A195095 A195096

Keyword

nonn,easy

Author

Harvey P. Dale, Sep 08 2011

Status

approved