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A182676 a(n) is the largest n-digit number with exactly 8 divisors, a(n) = 0 if no such number exists.

%I A182676 #25 Apr 09 2024 05:20:20
%S A182676 0,88,999,9994,99995,999994,9999994,99999994,999999998,9999999995,
%T A182676 99999999998,999999999998,9999999999998,99999999999998,
%U A182676 999999999999995,9999999999999998,99999999999999998,999999999999999987,9999999999999999995,99999999999999999985,999999999999999999995
%N A182676 a(n) is the largest n-digit number with exactly 8 divisors, a(n) = 0 if no such number exists.
%C A182676 a(n) is the largest 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.
%H A182676 Amiram Eldar, <a href="/A182676/b182676.txt">Table of n, a(n) for n = 1..100</a>
%F A182676 a(n) = max {10^(n-1) <= k < 10^n : A000005(k)=8} if set is nonempty, else a(n) = 0.
%p A182676 with(numtheory):
%p A182676 a:= proc(n) local k;
%p A182676       if n<2 then 0
%p A182676     else for k from 10^n-1 while tau(k)<>8 by -1
%p A182676          do od; k
%p A182676       fi
%p A182676     end:
%p A182676 seq(a(n), n=1..20);
%o A182676 (PARI) a(n)=forstep(k=10^n-1,10^(n-1),-1,numdiv(k)==8 & return(k)) \\ _M. F. Hasler_, Nov 27 2010
%Y A182676 Cf. A000005, A030626, A182675.
%K A182676 nonn,base
%O A182676 1,2
%A A182676 _Jaroslav Krizek_, Nov 27 2010
%E A182676 Edited by _Alois P. Heinz_, Nov 27 2010
%E A182676 Given terms double-checked with given PARI code by _M. F. Hasler_, Nov 27 2010
%E A182676 a(20)-a(21) from _Amiram Eldar_, Apr 09 2024