A045716 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

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

EXAMPLE

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]

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A029837, A002110, A046971, A054850.

Sequence in context: A218485 A310029 A310030 * A236203 A122539 A310031

Adjacent sequences: A045713 A045714 A045715 * A045717 A045718 A045719

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved