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a(n) = the smallest n-digit number with exactly 12 divisors, a(n) = 0 if no such number exists.
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%I #8 Mar 30 2012 19:00:24

%S 0,60,108,1012,10004,100004,1000012,10000025,100000012,1000000025,

%T 10000000012,100000000004,1000000000017,10000000000004,

%U 100000000000012,1000000000000004,10000000000000025,100000000000000004,1000000000000000017,10000000000000000034,100000000000000000012,1000000000000000000025,10000000000000000000004,100000000000000000000004

%N a(n) = the smallest n-digit number with exactly 12 divisors, a(n) = 0 if no such number exists.

%C a(n) = the smallest n-digit number of the form p^11, p^5*q, p^3*q^2 or p^2*q*r (p, q, r distinct primes), a(n) = 0 if no such number exists.

%F A000005(a(n)) = 12.

%F a(n) <= A182684(n).

%t Table[k=10^(n-1); While[k<10^n && DivisorSigma[0, k] != 12, k++]; If[k==10^n, k=0]; k, {n, 20}]

%Y Cf. A030630, A182684.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Nov 27 2010