A326677 - OEIS

%I #14 Oct 18 2019 18:33:52

%S 1,2,4,8,12,16,24,32,36,48,64,72,96,120,144,240,288,360,432,576,720,

%T 1080,1260,1440,2160,2520,2880,3600,5040,7200,7560,8640,10080,14400,

%U 15120,20160,25200,30240,40320,45360,50400,55440,75600,100800,110880,151200,166320

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

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

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

%H Amiram Eldar, <a href="/A326677/b326677.txt">Table of n, a(n) for n = 1..362</a>

%e 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.

%t 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 *)

%Y Cf. A002182, A025487, A169594.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 18 2019