A195091 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 7.

256, 768, 1152, 1280, 1728, 1792, 2592, 2816, 3200, 3328, 3840, 3888, 4352, 4864, 5376, 5760, 5832, 5888, 6272, 6561, 7424, 7936, 8000, 8064, 8448, 8640, 8748, 8960, 9472, 9600, 9984, 10496, 11008, 12032, 12096, 12672, 12960, 13056, 13122, 13568

Offset

1,1

Comments

The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0029589..., 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)) = 7. - Reinhard Zumkeller, Nov 29 2015

Mathematica

Select[Range[14000], PrimeOmega[#]-PrimeNu[#]==7&]

Prog

(PARI) is(n)=bigomega(n)-omega(n)==7 \\ Charles R Greathouse IV, Sep 14 2015
(Haskell)
a195091 n = a195091_list !! (n-1)
a195091_list = filter ((== 7) . a046660) [1..]
-- Reinhard Zumkeller, Nov 29 2015

Crossrefs

Cf. A060687, A195069, A195086, A195087, A195088, A195089, A195090, A195092, A195093.

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

Sequence in context: A237015 A237008 A045057 * A361176 A203450 A188248

Adjacent sequences: A195088 A195089 A195090 * A195092 A195093 A195094

Keyword

nonn,easy

Author

Harvey P. Dale, Sep 08 2011

Status

approved