A277758 The number of highly composite numbers between the factorials n! and (n+1)!.

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, 19, 17, 19, 20, 21, 17, 24, 20, 20, 21, 22, 22, 20, 26, 26, 24, 26, 29, 27, 28, 26, 27, 27, 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

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

Cf. A002182, A277760.

Sequence in context: A230421 A219641 A341464 * A240027 A203555 A096197

Adjacent sequences: A277755 A277756 A277757 * A277759 A277760 A277761

Keyword

nonn

Author

Greg Huber, Oct 29 2016

Extensions

Terms a(12) and beyond from Joerg Arndt, Nov 01 2016

Status

approved