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

Author

Harvey P. Dale, Sep 08 2011

Keywords

• nonn
• easy

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

Examples

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

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

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

Programs

Haskell

a195069 n = a195069_list !! (n-1)
a195069_list = filter ((== 10) . a046660) [1..]
-- Reinhard Zumkeller, Nov 29 2015

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&]

PARI

isok(n) = bigomega(n) - omega(n) == 10; \\ Michel Marcus, Jul 03 2018

Formula

A046660(a(n)) = 10. - Reinhard Zumkeller, Nov 29 2015