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

0, 0, 0, 4096, 0, 531441, 0, 0, 244140625, 0, 13841287201, 0, 3138428376721, 23298085122481, 582622237229761, 2213314919066161, 21914624432020321, 787662783788549761, 6582952005840035281, 39959630797262576401

Offset: 1

Author

Jaroslav Krizek, Nov 27 2010

Keywords

• nonn
• base

Comments

a(n) = the largest n-digit number of the form p^12 (p = prime), a(n) = 0 if no such number exists.

Links

• Robert Israel, Table of n, a(n) for n = 1..999

Crossrefs

Cf. A030631, A182685.

Programs

Maple

f:= proc(n) local r;
  r:= prevprime(ceil(10^(n/12)))^12;
  if r < 10^(n-1) then 0 else r fi;
end proc:
f(1):= 0: f(2):= 0: f(3):=0:
map(f, [$1..30]); # Robert Israel, Apr 03 2019

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

Formula

A000005(a(n)) = 13.

a(n) = A182685(n) for n <= 17.