A195069 Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 10.

2048, 6144, 9216, 10240, 13824, 14336, 20736, 22528, 25600, 26624, 30720, 31104, 34816, 38912, 43008, 46080, 46656, 47104, 50176, 59392, 63488, 64000, 64512, 67584, 69120, 69984, 71680, 75776, 76800, 79872, 83968, 88064, 96256, 96768, 101376, 103680, 104448

Offset

1,1

Comments

The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0003698..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - Amiram Eldar, Sep 25 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)) = 10. - Reinhard Zumkeller, Nov 29 2015

Example

14336 = 2^11 * 7^1, so it has 12 prime factors (counted with multiplicity) and 2 distinct prime factors, and 12-2 = 10.

Maple

op(select(n->bigomega(n)-nops(factorset(n))=10, [$1..104448])); # Paolo P. Lava, Jul 03 2018

Mathematica

Select[Range[200000], PrimeOmega[#] - PrimeNu[#] == 10&]

Prog

(Haskell)
a195069 n = a195069_list !! (n-1)
a195069_list = filter ((== 10) . a046660) [1..]
-- Reinhard Zumkeller, Nov 29 2015
(PARI) isok(n) = bigomega(n) - omega(n) == 10; \\ Michel Marcus, Jul 03 2018

Crossrefs

Cf. A025487, A060687, A195087, A195088, A195089, A195090, A195091, A195092, A195093.

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

Sequence in context: A069272 A234881 A220584 * A316499 A135290 A204837

Adjacent sequences: A195066 A195067 A195068 * A195070 A195071 A195072

Keyword

nonn,easy

Author

Harvey P. Dale, Sep 08 2011

Status

approved