Divisibility sequence

In mathematics, a divisibility sequence is an integer sequence such that for all natural numbers m, n,

i.e., whenever one index is a multiple of another one, then the corresponding term also is a multiple of the other term. The concept can be generalized to sequences with values in any ring where the concept of divisibility is defined.

A strong divisibility sequence is an integer sequence such that for all natural numbers m, n,

Note that a strong divisibility sequence is immediately a divisibility sequence; if , immediately . Then by the strong divisibility property, and therefore .

Examples

References

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