A352504 - OEIS

%I #17 Apr 27 2022 10:44:20

%S 2,12,15,16,18,20,24,28,30,32,36,40,45,48,54,56,60,64,72,80,84,90,96,

%T 108,112,120,128,140,144,160,168,180,192,200,210,216,224,240,252,256,

%U 270,280,288,300,320,336,360,384,400,420,432,448,480,504,512,540,560

%N Numbers k > 1 such that log(A005179(k))/k is a record low.

%C It appears that 15 and 45 are the only odd numbers in the sequence.

%C It also appears that this is a subsequence of A175495.

%H Lucas C. D. Jacobs, <a href="/A352504/b352504.txt">Table of n, a(n) for n = 1..442</a>

%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_ *)

%Y Cf. A005179, A175495.

%K nonn

%O 1,1

%A _Lucas C. D. Jacobs_, Mar 18 2022