A045716 - OEIS

%I #21 Jun 18 2018 04:13:59

%S 1,3,5,8,12,15,19,24,28,33,38,43,49,54,60,65,71,77,83,89,96,102,108,

%T 115,121,128,135,141,148,155,162,169,176,183,190,198,205,212,220,227,

%U 235,242,250,257,265,273,280,288,296,304,312,319,327,335,343,351,359

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

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

%H Michael De Vlieger, <a href="/A045716/b045716.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A070939(A002110(n)) for n>1. - _Jachym Barvinek_, Mar 22 2018

%e 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]

%t Table[Ceiling@ Log2[Times @@ Prime@ Range@ n], {n, 57}] (* _Michael De Vlieger_, Feb 05 2017 *)

%o (PARI) a(n)=logint(prod(i=1,n,prime(i))-1,2)+1 \\ _Charles R Greathouse IV_, Feb 06 2017

%Y Cf. A029837, A002110, A046971, A054850.

%K nonn

%O 1,2

%A _Labos Elemer_