[seqfan] About squarefree numbers (2^n-1)/gcd(n, 2^n-1) and (2^n+1)/gcd(n, 2^n+1)

[Tomasz Ordowski]

Dear SeqFans,

I formulated the following theorems (easy to prove):

The smallest numerator of (2^n-1) / n is not squarefree
if and only if n = k ord_q(2) for k = 1, 2, 3, ...;
where q is a Wieferich prime (1093 and 3511).

Cf. https://oeis.org/A272359

The smallest numerator of (2^n+1) / n is not squarefree
if and only if n = (2k+1) ord_q(2) / 2 for k = 0, 1, 2, ...;
where q is a Wieferich prime (1093).

Cf. https://oeis.org/A272361

Are these well-known facts?

Best regards,

Thomas
_______________
ord_1093(2) = 364,
ord_3511(2) = 1755;
i.e. A002326((q-1)/2).