A180922 Smallest n-digit number that is divisible by exactly 3 primes (counted with multiplicity).

8, 12, 102, 1001, 10002, 100006, 1000002, 10000005, 100000006, 1000000003, 10000000001, 100000000006, 1000000000001, 10000000000001, 100000000000018, 1000000000000002, 10000000000000006, 100000000000000007, 1000000000000000001, 10000000000000000007

Offset: 1

Author

Jonathan Vos Post, Jan 23 2011

Keywords

• nonn
• base
• easy

Comments

This is to 3 as smallest n-digit semiprime A098449 is to 2, and as smallest n-digit prime A003617 is to 1. Smallest n-digit triprime. Smallest n-digit 3-almost prime.

Examples

			a(1) = 8 because 8=2^3 is the smallest (only) 1-digit number divisible by exactly 3 primes (counted with multiplicity).
a(2) = 12 because 12 = 2^2 * 3 is the smallest of the (21) 2-digit numbers divisible by exactly 3 primes (counted with multiplicity).
a(3) = 102 because 102 = 2 * 3 * 17 is the smallest 3-digit numbers divisible by exactly 3 primes (counted with multiplicity).
		

Crossrefs

Cf. A003617, A014612, A098449.

Programs

PARI

A180922(n)=for(n=10^(n-1),10^n-1,bigomega(n)==3&return(n)) \\ M. F. Hasler, Jan 23 2011

Python

from sympy import factorint
def triprimes(n): f = factorint(n); return sum(f[p] for p in f) == 3
def a(n):
  an = max(1, 10**(n-1))
  while not triprimes(an): an += 1
  return an
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Apr 10 2021