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

1,1

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

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 *)

Crossrefs

Cf. A005179, A175495.

Sequence in context: A269130 A265485 A166745 * A262094 A200183 A118516

Adjacent sequences: A352501 A352502 A352503 * A352505 A352506 A352507

Keyword

nonn

Author

Lucas C. D. Jacobs, Mar 18 2022

Status

approved