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a(n) = the smallest n-digit number with exactly 6 divisors, a(n) = 0 if no such number exists.
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%I #10 Mar 30 2012 19:00:24

%S 0,12,116,1004,10012,100017,1000028,10000036,100000036,1000000017,

%T 10000000004,100000000017,1000000000028,10000000000036,

%U 100000000000019,1000000000000025,10000000000000091,100000000000000028,1000000000000000179,10000000000000000196

%N a(n) = the smallest n-digit number with exactly 6 divisors, a(n) = 0 if no such number exists.

%C a(n) = the smallest n-digit number of the form p^5 or p^2*q^1, (p, q = distinct primes), a(n) = 0 if no such number exists.

%F A000005(a(n)) = 6.

%t Table[k=10^(n-1); While[k<10^n && DivisorSigma[0, k] != 6, k++]; If[k==10^n, k=0]; k, {n, 10}]

%Y Cf. A182672 (largest n-digit number with exactly 6 divisors).

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Nov 27 2010

%E Extended by _T. D. Noe_, Nov 29 2010