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

1,2

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, ...

Links

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

Example

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.

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 *)

Crossrefs

Cf. A002093, A168512.

Sequence in context: A321266 A018662 A240557 * A191612 A362668 A048874

Adjacent sequences: A326709 A326710 A326711 * A326713 A326714 A326715

Keyword

nonn

Author

Amiram Eldar, Oct 18 2019

Status

approved