OFFSET
1,2
COMMENTS
The interval is taken to be the half-open interval [n!, (n+1)!).
LINKS
Joerg Arndt, Table of n, a(n) for n = 1..371
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) = 4 since the four highly composite numbers (A002182) in the interval [5!,6!) are 120, 180, 240, and 360.
MATHEMATICA
nn = 9; Table[Count[#, k_ /; n! <= k < (n + 1)!], {n, nn}] &[Block[{a = 0}, Reap[Do[b = DivisorSigma[0, k]; If[b > a, a = b; Sow[k]], {k, (nn + 1)!}]][[-1, 1]]]] (* Michael De Vlieger, Oct 31 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Greg Huber, Oct 29 2016
EXTENSIONS
Terms a(12) and beyond from Joerg Arndt, Nov 01 2016
STATUS
approved