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a(n) = the largest 2-digit number with exactly n divisors, a(n) = 0 if no such number exists.
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%I #7 May 24 2019 16:40:22

%S 0,97,49,95,81,99,64,88,36,80,0,96,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N a(n) = the largest 2-digit number with exactly n divisors, a(n) = 0 if no such number exists.

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

%F 12 = max n such that a(n) > 0, a(n) = 0 for n > 12.

%t With[{ds=Reverse[Table[{n,DivisorSigma[0,n]},{n,10,99}]]},Table[ SelectFirst[ ds,#[[2]]==k&],{k,50}]][[All,1]]/."NotFound"->0 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 24 2019 *)

%Y Cf. A182689.

%K nonn,base,less

%O 1,2

%A _Jaroslav Krizek_, Nov 27 2010