A182675 - OEIS

%I #20 Apr 23 2024 10:21:09

%S 0,24,102,1001,10002,100006,1000002,10000005,100000006,1000000003,

%T 10000000001,100000000006,1000000000001,10000000000001,

%U 100000000000018,1000000000000002,10000000000000006,100000000000000007,1000000000000000001,10000000000000000007,100000000000000000003

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

%C 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.

%C 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

%H Amiram Eldar, <a href="/A182675/b182675.txt">Table of n, a(n) for n = 1..100</a>

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

%p with (numtheory):

%p a:= proc(n) local k;

%p      if n<2 then 0

%p    else for k from 10^(n-1) while tau(k)<>8

%p         do od; k

%p      fi

%p     end:

%p seq (a(n), n=1..20);

%o (PARI) a(n) = for(k = 10^(n-1), 10^n-1, if(numdiv(k)==8, return(k))); 0; \\ _Amiram Eldar_, Apr 09 2024

%Y Cf. A000005, A030626, A182676, A180922.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Nov 27 2010

%E Edited by _Alois P. Heinz_, Nov 27 2010

%E a(20)-a(21) from _Amiram Eldar_, Apr 09 2024