A352504 Numbers k > 1 such that log(A005179(k))/k is a record low.

2, 12, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 45, 48, 54, 56, 60, 64, 72, 80, 84, 90, 96, 108, 112, 120, 128, 140, 144, 160, 168, 180, 192, 200, 210, 216, 224, 240, 252, 256, 270, 280, 288, 300, 320, 336, 360, 384, 400, 420, 432, 448, 480, 504, 512, 540, 560

Offset: 1

Author

Lucas C. D. Jacobs, Mar 18 2022

Keywords

• nonn

Comments

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

It also appears that this is a subsequence of A175495.

Links

• Lucas C. D. Jacobs, Table of n, a(n) for n = 1..442

Crossrefs

Cf. A005179, A175495.

Programs

Mathematica

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 *)