A243296 - OEIS

%I #12 Jun 03 2014 02:41:04

%S 3,5,4,3,4,4,3,3,4,4,3,3,4,4,3,5,3,4,5,4,4,3,3,3,8,4,3,4,4,4,3,3,6,3,

%T 3,4,3,3,4,3,4,4,4,3,3,6,7,3,5,4,4,4,3,3,3,5,9,3,3,6,3,7,4,9,3,6,5,3,

%U 6,7,4,4,3,5,5,3,5,7,4,3,4,4,4,5,3

%N Exponent of 2 in (A002110(n)/2)^2-1

%C a(n) >= 3, = 3 if A002110(n) == 6 or 10 mod 16.

%C Whenever A000040(n) is in A003629, at least one of a(n) and a(n+1) is 3.

%H Robert Israel, <a href="/A243296/b243296.txt">Table of n, a(n) for n = 2..10000</a>

%H MathOverflow question <a href="http://mathoverflow.net/questions/163241">On quantities with no very small odd prime factors; a response to Wlodzimierz Holsztynski</a>

%e A002110(2) = 2*3 = 6 and (6/2)^2-1 = 8 = 2^3 so a(2) = 3.

%p N:= 1000; # to get a(2) to a(N)

%p P:= 1:

%p for n from 2 to N do

%p   P:= P * ithprime(n);

%p   A[n]:= padic[ordp](P^2-1,2);

%p od:

%p seq(A[n],n=2..N); # _Robert Israel_, Jun 02 2014

%Y Cf. A002110.

%K nonn

%O 2,1

%A _Robert Israel_, Jun 02 2014