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%I #5 Oct 15 2013 22:31:01
%S 24,900,810000,729000000,590490000000000,531441000000000000,
%T 430467210000000000000000,387420489000000000000000000,
%U 313810596090000000000000000000000
%N Smallest number with p(n)^3 divisors where p(n) is n-th prime.
%F For p=2, 24 is the solution. If p>2 prime, then suitable powers of 30 are the least solutions: a(n)=Min{x|d(x)=A000005(x)=p(n)^3}=30^[p(n)-1], p(n)=n-th prime; d[2^(ppp-1)]=d[2^(pp-1)3^(p-1)]=d[30^(p-1)]=p^3 and 2^(ppp-1)>2^(pp-1)3^(p-1)>30^(p-1) holds if p>2.
%e p=2, then d(128)=d(24)=d(30)=8 and a(1)=24<30 is the smallest; P=5, then 2^124>(2^24)*(3^4)>30^4=810000=a(3).
%Y Cf. A000005, A005179, A003680, A037992, A061283, A061286, A061148, A061149.
%K nonn
%O 1,1
%A _Labos Elemer_, Jun 01 2001