A326807 Numbers m such that s(m)/m > s(k)/k for all k < m, where s(m) = A168512(m) is the sum of divisors of m, weighted by divisor multiplicity.

1, 2, 4, 8, 12, 16, 24, 36, 72, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800, 21621600, 36756720, 61261200, 73513440

Offset: 1

Author

Amiram Eldar, Oct 19 2019

Keywords

• nonn

Comments

The least number m such that A168512(m)/m > k, for k = 2, 3, ... is 4, 120, 27720, 122522400, ...

Crossrefs

Cf. A004394, A168512, A326677, A326712.

Programs

Mathematica

s[n_] := 1 + DivisorSum[n, #*IntegerExponent[n, #] &, # > 1 &]; seq = {}; sm = 0; Do[s1 = s[n]/n; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 100000000}]; seq (* after Michael De Vlieger at A168512 *)