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

Author

Harvey P. Dale, Sep 08 2011

Keywords

• nonn

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.

Crossrefs

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

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

Programs

Haskell

a195087 n = a195087_list !! (n-1)
a195087_list = filter ((== 3) . a046660) [1..]
-- Reinhard Zumkeller, Nov 29 2015

Mathematica

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

PARI

is(n)=bigomega(n)-omega(n)==3 \\ Charles R Greathouse IV, Sep 14 2015

Formula

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

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