|
%I #36 Nov 01 2016 05:01:06
%S 1,2,2,4,4,5,7,9,9,10,10,12,10,11,12,13,13,14,12,14,12,15,15,17,15,19,
%T 19,17,19,20,21,17,24,20,20,21,22,22,20,26,26,24,26,29,27,28,26,27,27,
%U 31,28,28,28,31,29,30,30,28,29,32,32,26,26,31,28,29,28,30,34,33,34,35,34,31,37,35,35,35,37,42,39,37,40
%N The number of highly composite numbers between the factorials n! and (n+1)!.
%C The interval is taken to be the half-open interval [n!, (n+1)!).
%H Joerg Arndt, <a href="/A277758/b277758.txt">Table of n, a(n) for n = 1..371</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) = 4 since the four highly composite numbers (A002182) in the interval [5!,6!) are 120, 180, 240, and 360.
%t 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 *)
%Y Cf. A002182, A277760.
%K nonn
%O 1,2
%A _Greg Huber_, Oct 29 2016
%E Terms a(12) and beyond from _Joerg Arndt_, Nov 01 2016
|
