A326677 Numbers with a record number of divisors, counted with multiplicity (A169594).

1, 2, 4, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 120, 144, 240, 288, 360, 432, 576, 720, 1080, 1260, 1440, 2160, 2520, 2880, 3600, 5040, 7200, 7560, 8640, 10080, 14400, 15120, 20160, 25200, 30240, 40320, 45360, 50400, 55440, 75600, 100800, 110880, 151200, 166320

Offset

1,2

Comments

The corresponding record values are 1, 2, 4, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 22, 24, 26, 28, 29, ...

Since the value of A169594(k) depends only on the prime signature of k, this sequence is a subsequence of A025487.

Links

Amiram Eldar, Table of n, a(n) for n = 1..362

Example

The first values of A169594(n) for n=1..8 are {1, 2, 2, 4, 2, 4, 2, 6}. The record values are 1, 2, 4, 6, for 1, 2, 4, 8. Therefore this sequence begins with 1, 2, 4, 8.

Mathematica

d[n_]:=1 + DivisorSum[n, IntegerExponent[n, #] &, # > 1 &]; s={}; dm = 0; Do[d1 = d[n]; If[d1 > dm, dm = d1; AppendTo[s, n]], {n, 1, 10000}]; s (* after Michael De Vlieger at A169594 *)

Crossrefs

Cf. A002182, A025487, A169594.

Sequence in context: A227730 A246692 A181824 * A330684 A070173 A363122

Adjacent sequences: A326674 A326675 A326676 * A326678 A326679 A326680

Keyword

nonn

Author

Amiram Eldar, Oct 18 2019

Status

approved