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%I #26 Jul 27 2021 12:10:46
%S 1,2,4,8,16,450,64,128,36,162,1024,1800,4096,1458,144,32768,65536,
%T 54450,262144,405000,576,118098,4194304,28800,1296,1062882,900,5832,
%U 268435456,115200,1073741824,2147483648,9216,86093442,5184,217800,68719476736,774840978,102400
%N Least k >= 1 such that sigma(k)/tau(k) has denominator n or zero if no k exists.
%C Conjecture: k always exists.
%t seq[max_] := Module[{s = Table[0,{max}], c = 0, n = 1}, While[c < max, d = Denominator[DivisorSigma[1,n]/DivisorSigma[0,n]]; If[d <= max && s[[d]] == 0, c++; s[[d]] = n]; n++]; s]; seq[22] (* _Amiram Eldar_, Jul 26 2021 *)
%o (PARI) a(n)=if(n<0, 0, t=1; while(denominator(sigma(t)/numdiv(t))!=n, t++); t)
%Y Cf. A057020, A057021, A069081.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jul 26 2021
%E a(29)-a(36) from _Amiram Eldar_, Jul 26 2021
%E a(37) from _David A. Corneth_, Jul 26 2021
%E a(38)-a(39) from _Jinyuan Wang_, Jul 26 2021
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