A195087 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 3.

16, 48, 72, 80, 81, 108, 112, 162, 176, 200, 208, 240, 272, 304, 336, 360, 368, 392, 405, 464, 496, 500, 504, 528, 540, 560, 567, 592, 600, 624, 625, 656, 675, 688, 752, 756, 792, 810, 816, 848, 880, 891, 900, 912, 936, 944, 968, 976

Offset

1,1

Comments

The asymptotic density of this sequence is (Sum_{p prime} 1/(p^3*(p+1)) + Sum_{p != q primes} 1/(p^2*(p+1)*q*(q+1)) + Sum_{p < q < r primes} 1/(p*(p+1)*q*(q+1)*r*(r+1)))/zeta(2) = 0.04761... . - Amiram Eldar, Sep 03 2022

Links

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

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

Formula

A001222(a(n)) - A001221(a(n)) = 3.

A046660(a(n)) = 3. - Reinhard Zumkeller, Nov 29 2015

Mathematica

Select[Range[1000], PrimeOmega[#]-PrimeNu[#]==3&]

Prog

(PARI) is(n)=bigomega(n)-omega(n)==3 \\ Charles R Greathouse IV, Sep 14 2015
(Haskell)
a195087 n = a195087_list !! (n-1)
a195087_list = filter ((== 3) . a046660) [1..]
-- Reinhard Zumkeller, Nov 29 2015

Crossrefs

Cf. A001221, A001222, A060687, A195069, A195086, A195088, A195089, A195090, A195091, A195092, A195093.

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

Sequence in context: A264164 A045047 A239344 * A348882 A130897 A374589

Adjacent sequences: A195084 A195085 A195086 * A195088 A195089 A195090

Keyword

nonn

Author

Harvey P. Dale, Sep 08 2011

Status

approved