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%I #16 May 24 2016 03:37:13
%S 1,3,9,15,16,32,0,56,36,80,0,140,0,192,144,216,0,300,0,336,0,0,0,540,
%T 0,0,0,0,0,720,0,840,0,0,0,1260,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N a(n) = greatest number k <= n^2 having exactly n divisors, or 0 if no such k exists.
%C The sequence is zero for n>36, since A005179(n) > n^2 for all n > 36.
%e a(4) = 15, because 15 is the greatest number <= 4^2 with exactly 4 divisors.
%t Seq := {}; For[n = 1, n < 50, n++, AppendTo[Seq, a = Max[Select[Range[n^2], DivisorSigma[0, #] == n &]]; If[a == -Infinity, 0, a]]]; Seq
%Y Cf. A000005, A005179, A035033.
%K nonn,easy
%O 1,2
%A _Carlos Eduardo Olivieri_, May 20 2016