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

1,2

Comments

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

Links

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

Formula

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

Maple

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);

Prog

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

Crossrefs

Cf. A000005, A030626, A182676, A180922.

Sequence in context: A213842 A333033 A269047 * A100155 A304415 A268804

Adjacent sequences: A182672 A182673 A182674 * A182676 A182677 A182678

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Extensions

Edited by Alois P. Heinz, Nov 27 2010

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

Status

approved