A036761 Number of refactorable integers (A033950) of binary order (A029837) n.

1, 1, 0, 1, 2, 2, 4, 8, 13, 22, 39, 77, 137, 254, 459, 889, 1665, 3175, 6041, 11619, 22319, 42979, 83123, 160649, 311826, 605225, 1176998, 2291702, 4466923, 8716126, 17023771, 33279942, 65109458, 127484313, 249783733, 489738130, 960801221, 1886039740

Offset

0,5

Comments

Since for any epsilon d(n) <= n^epsilon if n is large enough, a(n) does not grow very quickly.

Links

Table of n, a(n) for n=0..37.

Example

{1} has binary order 0, {2} has binary order 1, no term has binary order 2, {8} has binary order 3, {9,12} have binary order 4, {18,24} have binary order 5, ...
The 8 numbers, between 65 and 128 (with binary order 7) which are divided by d(x) (A000005) are 72,80,84,88,96,104,108,128, so a(7)=8.

Maple

with(numtheory): A036761 := proc(n) local ct, k, lim: if(n=0)then return 1: else ct:=0: lim:=2^n: for k from 2^(n-1)+1 to lim do if(k mod tau(k) = 0)then ct:=ct+1: fi: od: return ct: fi: end: seq(A036761(n), n=0..10); # Nathaniel Johnston, May 04 2011

Mathematica

Table[Count[Range[2^(n - 1) + 1, 2^(n)], k_ /; Divisible[k, DivisorSigma[0, k]]] + Boole[n == 0], {n, 0, 22}] (* Michael De Vlieger, May 20 2017 *)

Crossrefs

Cf. A000005, A029837, A033950.

Sequence in context: A323865 A104700 A039941 * A042979 A000018 A357307

Adjacent sequences: A036758 A036759 A036760 * A036762 A036763 A036764

Keyword

nonn

Author

Labos Elemer

Extensions

a(22)-a(37) from Donovan Johnson, Aug 29 2012

Status

approved