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.

%I A182675 #20 Apr 23 2024 10:21:09
%S A182675 0,24,102,1001,10002,100006,1000002,10000005,100000006,1000000003,
%T A182675 10000000001,100000000006,1000000000001,10000000000001,
%U A182675 100000000000018,1000000000000002,10000000000000006,100000000000000007,1000000000000000001,10000000000000000007,100000000000000000003
%N A182675 a(n) is the smallest n-digit number with exactly 8 divisors, a(n) = 0 if no such number exists.
%C A182675 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 A182675 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 A182675 Amiram Eldar, <a href="/A182675/b182675.txt">Table of n, a(n) for n = 1..100</a>
%F A182675 a(n) = min {10^(n-1) <= k < 10^n : A000005(k)=8} if set is nonempty, else a(n) = 0.
%p A182675 with (numtheory):
%p A182675 a:= proc(n) local k;
%p A182675      if n<2 then 0
%p A182675    else for k from 10^(n-1) while tau(k)<>8
%p A182675         do od; k
%p A182675      fi
%p A182675     end:
%p A182675 seq (a(n), n=1..20);
%o A182675 (PARI) a(n) = for(k = 10^(n-1), 10^n-1, if(numdiv(k)==8, return(k))); 0; \\ _Amiram Eldar_, Apr 09 2024
%Y A182675 Cf. A000005, A030626, A182676, A180922.
%K A182675 nonn,base
%O A182675 1,2
%A A182675 _Jaroslav Krizek_, Nov 27 2010
%E A182675 Edited by _Alois P. Heinz_, Nov 27 2010
%E A182675 a(20)-a(21) from _Amiram Eldar_, Apr 09 2024