A045716 a(n) is the binary order (A029837) of the n-th primorial number, A002110(n).

1, 3, 5, 8, 12, 15, 19, 24, 28, 33, 38, 43, 49, 54, 60, 65, 71, 77, 83, 89, 96, 102, 108, 115, 121, 128, 135, 141, 148, 155, 162, 169, 176, 183, 190, 198, 205, 212, 220, 227, 235, 242, 250, 257, 265, 273, 280, 288, 296, 304, 312, 319, 327, 335, 343, 351, 359

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

These orders determine the maximal numbers of unitary divisors valid for integers in given binary order ranges (see A046971).

Examples

			The sixth primorial number is 2*3*5*7*11*13 = 30030, which is in the interval [16385, 32768] = [2^14 + 1, 2^15], so its binary order is a(6)=15. [corrected by _Jon E. Schoenfield_, May 13 2018]
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A029837, A002110, A046971, A054850.

Programs

Mathematica

Table[Ceiling@ Log2[Times @@ Prime@ Range@ n], {n, 57}] (* Michael De Vlieger, Feb 05 2017 *)

PARI

a(n)=logint(prod(i=1,n,prime(i))-1,2)+1 \\ Charles R Greathouse IV, Feb 06 2017

Formula

a(n) = A054850(n)+1, n >= 2.

a(n) = A070939(A002110(n)) for n>1. - Jachym Barvinek, Mar 22 2018