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(number theory, algebra) Any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ.

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divisibility sequence

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divisibility sequence

noun

The divisibility sequence is a fundamental concept in number theory.

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If 𝒞=(C_n)_(n>1) is any divisibility sequence, one says that a prime p is a primitive divisor of C_n if p|C_n but p∤C_1C_2C_n-1. Primitive divisors of certain divisibility sequences were studied by Zsigmondy [37] in the 19ᵗʰ century.

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divisibility sequence

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