%I #14 Nov 05 2020 15:08:11
%S 1,2,4,6,12,24,60,120,240,360,840,1680,2520,7560,15120,27720,55440,
%T 110880,221760,498960,720720,1441440,3603600,7207200,14414400,
%U 32432400,61261200,122522400,245044800,367567200,735134400,2095133040
%N a(n) is the minimal number of binary order n which has maximal number of divisors in this interval.
%C Compare with A007416, where terms of this sequence are present.
%e For n=9, with 256 < k <= 512, d(k) takes 17 distinct values, of which d(k)=24 is the greatest (see A036451 and A036470) and occurs first at k=360, so a(9)=360.
%t Block[{nn = 22, s}, s = TakeList[Array[DivisorSigma[0, # + 1] &, 2^nn - 1], 2^Range[0, nn - 1]]; {1}~Join~Map[2^(#1 - 1) + #2 & @@ FirstPosition[s, #] &, Map[Max, s]]] (* _Michael De Vlieger_, Nov 04 2020 *)
%Y Cf. A000005, A029837, A005179, A007416, A036470, A036492, A036493.
%K nonn,more
%O 0,2
%A _Labos Elemer_
%E a(22)-a(31) from _Sean A. Irvine_, Nov 04 2020