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

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, 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, 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

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

Cf. A002182, A277758.

Sequence in context: A342255 A112377 A354521 * A371572 A127704 A307662

Adjacent sequences: A277757 A277758 A277759 * A277761 A277762 A277763

Keyword

nonn

Author

Greg Huber, Oct 29 2016

Extensions

Terms a(27) and beyond from Joerg Arndt, Nov 01 2016

Status

approved