A023395 - OEIS

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A023395

Only Fermat number divisible by A023394(n) is 2^2^a(n) + 1.

0, 1, 2, 3, 5, 4, 12, 6, 11, 11, 9, 5, 18, 12, 10, 12, 23, 16, 15, 10, 19, 12, 19, 13, 36, 21, 38, 32, 25, 17, 39, 6, 26, 27, 30, 30, 8, 12, 15, 29, 38, 7, 25, 27, 36, 42, 25, 13, 13, 55

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OFFSET

1,3

COMMENTS

From Jianing Song, Mar 02 2021: (Start)

2^(a(n)+1) is the multiplicative order of 2 modulo A023394(n).

Each k occurs A046052(k) times in this sequence provided that F(k) = 2^2^k + 1 is squarefree (no counterexamples are known). (End)

Alternatively, a(n) is the only k such that A023394(n) divides A000215(k). - Lorenzo Sauras Altuzarra, Feb 01 2023

LINKS

Table of n, a(n) for n=1..50.

Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m

Lorenzo Sauras-Altuzarra, Some properties of the factors of Fermat numbers, Art Discrete Appl. Math. (2022).