OFFSET
1,1
COMMENTS
Numbers divisible by the squares of exactly five distinct primes.
The asymptotic density of this sequence is (eta_1^5 - 10*eta_1^3*eta_2 + 15*eta_1*eta_2^2 + 20*eta_1^2*eta_3 - 20*eta_2*eta_3 - 30*eta_1*eta_4 + 24*eta_5)/(20*Pi^2) = 0.0000015673..., where eta_j = Sum_{p prime} 1/(p^2-1)^j (Pomerance and Schinzel, 2011).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Carl Pomerance and Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2011), pp. 52-66. See pp. 61-62.
EXAMPLE
5336100 = 2^2 * 3^2 * 5^2 * 7^2 * 11^2 is a term since it has exactly 5 prime factors, 2, 3, 5, 7 and 11, that are non-unitary.
MATHEMATICA
Select[Range[2*10^7], Count[FactorInteger[#][[;; , 2]], _?(#1 > 1 &)] == 5 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2020
STATUS
approved