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a(n) is the smallest 5-digit number with exactly n divisors, or a(n) = 0 if no such number exists.
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%I #16 Nov 07 2020 11:23:20

%S 0,10007,10201,10001,14641,10012,15625,10002,11236,10096,59049,10004,

%T 0,10048,13456,10005,65536,10092,0,10064,10816,11264,0,10008,10000,

%U 12288,10404,10176,0,10044,0,10010,25600,0,11664,10140,0,0,36864,10032,0,10944,0,15360

%N a(n) is the smallest 5-digit number with exactly n divisors, or a(n) = 0 if no such number exists.

%H Jinyuan Wang, <a href="/A182697/b182697.txt">Table of n, a(n) for n = 1..128</a>

%F A000005(a(n)) = n for a(n) > 0.

%F 128 = max n such that a(n) > 0, a(n) = 0 for n > 128.

%t Flatten[If[#=={},0,#]&/@Table[Select[Range[10000,99999],DivisorSigma[0,#]==n&,1],{n,30}]] (* _Harvey P. Dale_, Oct 17 2012 *)

%Y Cf. A182698 (the largest 5-digit number with exactly n divisors).

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Nov 27 2010

%E Corrected by _Harvey P. Dale_, Oct 17 2012