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%I #8 Jul 29 2016 08:41:44
%S 1,4,3,9,8,12,8,10,12,18,8,20,8,18,24,8,8,0,8,24,24,18,8,16,9,18,0,20,
%T 8,0,8,14,24,18,36,24,8,18,24,16,8,40,8,20,0,18,8,24,9,36,24,20,8,18,
%U 36,16,24,18,8,32,8,18,0,0,36,40,8,20,24,48
%N Least k such that d(k*n) = k, or 0 if no such k exists (d = A000005).
%e a(4) = 9 because A000005(9*4) = 9.
%t up[t_] := If[t < 15, 18, t^(1.066/Log[Log[t]])]; a[n_] := Catch@ Block[{k = 1}, While[ up[k*n]/k > 1, If[ DivisorSigma[0, k n] == k, Throw@ k, k++]]; 0]; Array[a, 70] (* _Giovanni Resta_, Jul 29 2016 *)
%Y Cf. A000005, A036763.
%K nonn
%O 1,2
%A _Altug Alkan_, Jul 29 2016