A326712 Numbers with a record sum of divisors, weighted by divisor multiplicity (A168512).

1, 2, 3, 4, 6, 8, 12, 16, 18, 20, 24, 30, 32, 36, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 210, 216, 240, 288, 300, 324, 336, 360, 420, 480, 504, 540, 576, 600, 660, 672, 720, 840, 900, 960, 1008, 1080, 1200, 1260, 1440, 1560, 1620, 1680, 1800, 1920, 1980, 2016

Offset: 1

Author

Amiram Eldar, Oct 18 2019

Keywords

• nonn

Comments

The corresponding record values are 1, 3, 4, 9, 12, 19, 30, 41, 42, 44, 64, 72, 75, 102, 134, 170, 208, 226, 237, 264, 294, ...

Examples

			The first values of A168512(n) for n=1..8 are {1, 3, 4, 9, 6, 12, 8, 19}. The record values are 1, 3, 4, 9, 12, 19 for 1, 2, 3, 4, 6, 8. Therefore this sequence begins with 1, 2, 3, 4, 6, 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A002093, A168512.

Programs

Mathematica

s[n_] := 1 + DivisorSum[n, #*IntegerExponent[n, #] &, # > 1 &]; seq = {}; sm = 0; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 100000}]; seq (* after Michael De Vlieger at A168512 *)