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

Author

Amiram Eldar, Oct 18 2019

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A002182, A025487, A169594.

Programs

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 *)