OFFSET
1,2
COMMENTS
The interval is taken to be the half-open interval [2^n,2^(n+1)).
LINKS
Joerg Arndt, Table of n, a(n) for n = 1..2647
P. Erdős, On Highly composite numbers, J. London Math. Soc. 19 (1944), 130--133 MR7,145d; Zentralblatt 61,79.
S. Ramanujan, Highly composite numbers, Proceedings of the London Mathematical Society, 2, XIV, 1915, 347 - 409.
EXAMPLE
a(5) = 3 since the set of highly composite numbers (A002182) between 32 and 64 is {36,48,60}.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Greg Huber, Oct 29 2016
EXTENSIONS
Terms a(27) and beyond from Joerg Arndt, Nov 01 2016
STATUS
approved