A243296 Exponent of 2 in (A002110(n)/2)^2-1.

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, 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, 6, 7, 4, 4, 3, 5, 5, 3, 5, 7, 4, 3, 4, 4, 4, 5, 3

Offset

2,1

Comments

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

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

Links

Robert Israel, Table of n, a(n) for n = 2..10000

MathOverflow question On quantities with no very small odd prime factors; a response to Wlodzimierz Holsztynski

Example

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

Maple

N:= 1000; # to get a(2) to a(N)
P:= 1:
for n from 2 to N do
  P:= P * ithprime(n);
  A[n]:= padic[ordp](P^2-1, 2);
od:
seq(A[n], n=2..N); # Robert Israel, Jun 02 2014

Crossrefs

Cf. A002110.

Sequence in context: A340256 A354247 A349943 * A081361 A195132 A086181

Adjacent sequences: A243293 A243294 A243295 * A243297 A243298 A243299

Keyword

nonn

Author

Robert Israel, Jun 02 2014

Status

approved