A326807 - OEIS

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.

%I #9 Oct 20 2019 22:05:35

%S 1,2,4,8,12,16,24,36,72,120,180,240,360,720,840,1260,1680,2520,5040,

%T 10080,15120,25200,27720,55440,110880,166320,277200,332640,554400,

%U 665280,720720,1441440,2162160,3603600,4324320,7207200,8648640,10810800,21621600,36756720,61261200,73513440

%N 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.

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

%t 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 *)

%Y Cf. A004394, A168512, A326677, A326712.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 19 2019