

A180922


Smallest ndigit number that is divisible by exactly 3 primes (counted with multiplicity).


3



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

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..20.


EXAMPLE

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


PROG

(PARI) A180922(n)=for(n=10^(n1), 10^n1, 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**(n1))
while not triprimes(an): an += 1
return an
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Apr 10 2021


CROSSREFS

Cf. A003617, A014612, A098449.
Sequence in context: A098664 A266800 A230545 * A083128 A196077 A067923
Adjacent sequences: A180919 A180920 A180921 * A180923 A180924 A180925


KEYWORD

nonn,base,easy


AUTHOR

Jonathan Vos Post, Jan 23 2011


STATUS

approved



