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a(n) = the smallest n-digit number with exactly 9 divisors, a(n) = 0 if no such number exists.
1

%I #13 Mar 30 2012 19:00:24

%S 0,36,100,1089,11236,101761,1006009,10023556,100020001,1000520161,

%T 10000200001,100000780441,1000002000001,10000021122961,

%U 100000020000001,1000000341419524,10000000200000001,100000004416539529,1000000012000000036,10000000017908741569,100000000060000000009,1000000000083244219609,10000000001400000000049,100000000002632322172441,1000000000014000000000049

%N a(n) = the smallest n-digit number with exactly 9 divisors, a(n) = 0 if no such number exists.

%C a(n) = the smallest n-digit number of the form p^8 or p^2*q^2 (p, q = distinct primes), a(n) = 0 if no such number exists.

%F A000005(a(n)) = 9.

%t Table[k=10^(n-1); While[k<10^n && DivisorSigma[0,k] != 9, k++]; If[k==10^n, k=0]; k, {n, 20}]

%Y See A182678(n) - the largest n-digit number with exactly 9 divisors.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Nov 27 2010

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

%E a(11)-a(25) from _Robert Gerbicz_, Nov 29 2010