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A277760 The number of highly composite numbers between 2^n and 2^(n+1). 2

%I

%S 1,2,1,1,3,1,2,1,2,2,1,2,2,3,3,2,2,3,3,2,3,3,3,3,3,3,3,2,3,3,4,3,2,2,

%T 3,4,3,3,2,4,3,2,3,4,4,3,2,2,4,4,3,2,2,4,3,4,2,3,4,3,4,3,3,3,3,3,2,3,

%U 2,4,3,3,4,4,4,3,3,2,4,3,4,3,3,2,4,4,4,4,5,3,4,4,4,4,4,4,4,3,3,3,4,5,4,4,3,3,4,4,4,4,5,3,4,4,4,4,5,2,4,4,5,3,5,3,4,6,4,3,4,4,5,5,4,3,3,4,5,4

%N The number of highly composite numbers between 2^n and 2^(n+1).

%C The interval is taken to be the half-open interval [2^n,2^(n+1)).

%H Joerg Arndt, <a href="/A277760/b277760.txt">Table of n, a(n) for n = 1..2647</a>

%H P. Erdős, <a href="https://www.renyi.hu/~p_erdos/1944-04.pdf">On Highly composite numbers</a>, J. London Math. Soc. 19 (1944), 130--133 MR7,145d; Zentralblatt 61,79.

%H S. Ramanujan, <a href="http://ramanujan.sirinudi.org/Volumes/published/ram15.html">Highly composite numbers</a>, Proceedings of the London Mathematical Society, 2, XIV, 1915, 347 - 409.

%e a(5) = 3 since the set of highly composite numbers (A002182) between 32 and 64 is {36,48,60}.

%t nn = 20; Table[Count[#, k_ /; 2^n <= k < 2^(n + 1)], {n, nn}] &[Block[{a = 0}, Reap[Do[b = DivisorSigma[0, k]; If[b > a, a = b; Sow[k]], {k, 2^(nn + 1)}]][[-1, 1]]]] (* _Michael De Vlieger_, Oct 31 2016 *)

%Y Cf. A002182, A277758.

%K nonn

%O 1,2

%A _Greg Huber_, Oct 29 2016

%E Terms a(27) and beyond from _Joerg Arndt_, Nov 01 2016

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)