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`%I #17 Apr 27 2022 10:44:20
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`%S 2,12,15,16,18,20,24,28,30,32,36,40,45,48,54,56,60,64,72,80,84,90,96,
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`%T 108,112,120,128,140,144,160,168,180,192,200,210,216,224,240,252,256,
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`%U 270,280,288,300,320,336,360,384,400,420,432,448,480,504,512,540,560
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`%N Numbers k > 1 such that log(A005179(k))/k is a record low.
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`%C It appears that 15 and 45 are the only odd numbers in the sequence.
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`%C It also appears that this is a subsequence of A175495.
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`%H Lucas C. D. Jacobs, <a href="/A352504/b352504.txt">Table of n, a(n) for n = 1..442</a>
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`%t mp[1, m_] := {{}}; mp[n_, 1] := {{}}; mp[n_?PrimeQ, m_] := If[m < n, {}, {{n}}]; mp[n_, m_] := Join @@ Table[Map[Prepend[#, d] &, mp[n/d, d]], {d, Select[Rest[Divisors[n]], # <= m &]}]; mp[n_] := mp[n, n]; values = Table[mulpar = mp[n] - 1; Min[Table[Product[Prime[s]^mulpar[[j, s]], {s, 1, Length[mulpar[[j]]]}], {j, 1, Length[mulpar]}]], {n, 1, 560}]; a = {}; min = 1; Do[ratio = Log[values[[i]]]/i; If[ratio < min, min = ratio; AppendTo[a, i]], {i, 2, Length[values]}]; a (* using code from _Vaclav Kotesovec_ *)
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`%Y Cf. A005179, A175495.
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`%K nonn
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`%O 1,1
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`%A _Lucas C. D. Jacobs_, Mar 18 2022
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