A180922 -id:A180922 - cp's OEIS frontend

A182675 a(n) is the smallest n-digit number with exactly 8 divisors, a(n) = 0 if no such number exists.

0, 24, 102, 1001, 10002, 100006, 1000002, 10000005, 100000006, 1000000003, 10000000001, 100000000006, 1000000000001, 10000000000001, 100000000000018, 1000000000000002, 10000000000000006, 100000000000000007, 1000000000000000001, 10000000000000000007, 100000000000000000003

Offset: 1

Jaroslav Krizek, Nov 27 2010

a(n) is the smallest n-digit number of the form p^7, p^3*q or p*q*r (p, q, r = distinct primes), a(n) = 0 if no such number exists.

There is a large overlap with A180922 because the candidates p*q*r are also of the 3-almost-primes format required there. - R. J. Mathar, Apr 23 2024

Amiram Eldar, Table of n, a(n) for n = 1..100

Cf. A000005, A030626, A182676, A180922.

with (numtheory):
a:= proc(n) local k;
     if n<2 then 0
   else for k from 10^(n-1) while tau(k)<>8
        do od; k
     fi
    end:
seq (a(n), n=1..20);

a(n) = for(k = 10^(n-1), 10^n-1, if(numdiv(k)==8, return(k))); 0; \\ Amiram Eldar, Apr 09 2024

a(n) = min {10^(n-1) <= k < 10^n : A000005(k)=8} if set is nonempty, else a(n) = 0.

Edited by Alois P. Heinz, Nov 27 2010

a(20)-a(21) from Amiram Eldar, Apr 09 2024

A180927 Largest n-digit number that is divisible by exactly 3 primes (counted with multiplicity).

Original entry on oeis.org

8, 99, 994, 9994, 99997, 999994, 9999994, 99999994, 999999998, 9999999995, 99999999998, 999999999998, 9999999999998, 99999999999998, 999999999999995, 9999999999999998, 99999999999999998, 999999999999999987, 9999999999999999999

Offset: 1

Jonathan Vos Post, Jan 23 2011

This is to 3 and A014612, as 2 and A098450 (largest n-digit semiprime), and as 1 and A003618 (largest n-digit prime). Largest n-digit triprime. Largest n-digit 3-almost prime.

			a(1) = 8 because 8 = 2^3 is the largest (only) 1-digit number that is divisible by exactly 3 primes (counted with multiplicity).
a(2) = 99 because 99 = 3^2 * 11 is the largest 2-digit number (of 21) that is divisible by exactly 3 primes (counted with multiplicity).
a(3) = 994 because 994 = 2 * 7 * 71 is the largest 3-digit number that is divisible by exactly 3 primes (counted with multiplicity).

Cf. A003618, A014612, A098450, A180922.

lndn3[n_]:=Module[{k=10^n-1},While[PrimeOmega[k]!=3,k--];k]; Array[ lndn3,20] (* Harvey P. Dale, Jul 25 2019 *)

A180927(n)=forstep(n=10^n-1,10^(n-1),-1,bigomega(n)==3&return(n)) \\ M. F. Hasler, Jan 23 2011

cp's OEIS Frontend

A182675 a(n) is the smallest n-digit number with exactly 8 divisors, a(n) = 0 if no such number exists.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

PARI

Formula

Extensions