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The acronym OEIS stands for the On-Line Encyclopedia of Integer Sequences, a well-known database of sequences of integers. It can be used for questions where this database is (or might be) relevant, mainly questions about particular sequences of integers. This tag is typically used in combination with other tags to make the scope of the question more precise; common examples of such tags include the top-level tags co.combinatorics and nt.number-theory.
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Are all counterexamples of OEIS A226181 both Poulet numbers and Proth numbers?
The answer is no, they aren't necessarily Proth numbers.
Consider $$n=7816642561=7\times 13\times 5581\times 15391 = 238545\times 2^{15}+1$$ for which we have $\mathrm{ord}_{n}(2)=954180 = (n-1)/2^{1 …