A195090 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 6.

128, 384, 576, 640, 864, 896, 1296, 1408, 1600, 1664, 1920, 1944, 2176, 2187, 2432, 2688, 2880, 2916, 2944, 3136, 3712, 3968, 4000, 4032, 4224, 4320, 4374, 4480, 4736, 4800, 4992, 5248, 5504, 6016, 6048, 6336, 6480, 6528, 6784

Offset

1,1

Comments

The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0059189..., 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)) = 6. - Reinhard Zumkeller, Nov 29 2015

Maple

op(select(n->bigomega(n)-nops(factorset(n))=6, [$1..6784])); # Paolo P. Lava, Jul 03 2018

Mathematica

Select[Range[7000], PrimeOmega[#]-PrimeNu[#]==6&]

Prog

(PARI) is(n)=bigomega(n)-omega(n)==6 \\ Charles R Greathouse IV, Sep 14 2015
(Haskell)
a195090 n = a195090_list !! (n-1)
a195090_list = filter ((== 6) . a046660) [1..]
-- Reinhard Zumkeller, Nov 29 2015

Crossrefs

Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195091, A195092, A195093.

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

Sequence in context: A086059 A220582 A203449 * A209380 A135271 A369638

Adjacent sequences: A195087 A195088 A195089 * A195091 A195092 A195093

Keyword

nonn,easy

Author

Harvey P. Dale, Sep 08 2011

Status

approved