cp's OEIS Frontend

A182686 a(n) = the largest n-digit number with exactly 13 divisors, a(n) = 0 if no such number exists.

%I A182686 #10 Apr 04 2019 03:00:06
%S A182686 0,0,0,4096,0,531441,0,0,244140625,0,13841287201,0,3138428376721,
%T A182686 23298085122481,582622237229761,2213314919066161,21914624432020321,
%U A182686 787662783788549761,6582952005840035281,39959630797262576401
%N A182686 a(n) = the largest n-digit number with exactly 13 divisors, a(n) = 0 if no such number exists.
%C A182686 a(n) = the largest n-digit number of the form p^12 (p = prime), a(n) = 0 if no such number exists.
%H A182686 Robert Israel, <a href="/A182686/b182686.txt">Table of n, a(n) for n = 1..999</a>
%F A182686 A000005(a(n)) = 13.
%F A182686 a(n) = A182685(n) for n <= 17.
%p A182686 f:= proc(n) local r;
%p A182686   r:= prevprime(ceil(10^(n/12)))^12;
%p A182686   if r < 10^(n-1) then 0 else r fi;
%p A182686 end proc:
%p A182686 f(1):= 0: f(2):= 0: f(3):=0:
%p A182686 map(f, [$1..30]); # _Robert Israel_, Apr 03 2019
%o A182686 (PARI) a(n) = my(r=precprime(ceil(10^(n/12))-1)^12); if(r < 10^(n-1), return(0)); r \\ Adapted from Robert Israel's Maple program; _Felix Fröhlich_, Apr 03 2019
%Y A182686 Cf. A030631, A182685.
%K A182686 nonn,base
%O A182686 1,4
%A A182686 _Jaroslav Krizek_, Nov 27 2010