What does divisibility sequence mean?
Definitions for divisibility sequence
di·vis·i·bil·i·ty se·quence
This dictionary definitions page includes all the possible meanings, example usage and translations of the word divisibility sequence.
Wiktionary
divisibility sequencenoun
A sequence of integers having the property that, if their respective positions in the sequence divide, then their values divide
Wikipedia
Divisibility sequence
In mathematics, a divisibility sequence is an integer sequence ( a n ) {\displaystyle (a_{n})} indexed by positive integers n such that if m ∣ n then a m ∣ a n {\displaystyle {\text{if }}m\mid n{\text{ then }}a_{m}\mid a_{n}} for all m, n. That is, 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 ( a n ) {\displaystyle (a_{n})} such that for all positive integers m, n, gcd ( a m , a n ) = a gcd ( m , n ) . {\displaystyle \gcd(a_{m},a_{n})=a_{\gcd(m,n)}.} Every strong divisibility sequence is a divisibility sequence: gcd ( m , n ) = m {\displaystyle \gcd(m,n)=m} if and only if m ∣ n {\displaystyle m\mid n} . Therefore by the strong divisibility property, gcd ( a m , a n ) = a m {\displaystyle \gcd(a_{m},a_{n})=a_{m}} and therefore a m ∣ a n {\displaystyle a_{m}\mid a_{n}} .
Numerology
Chaldean Numerology
The numerical value of divisibility sequence in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of divisibility sequence in Pythagorean Numerology is: 4
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"divisibility sequence." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/divisibility+sequence>.
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