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completely multiplicative function (another Prime Pages' Glossary entries) |
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Glossary:
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A function f(n) defined on the positive integers
is completely multiplicative if
f(nm)=f(n)f(m)
for all pairs n and m (compare this with
multiplicative functions). Three simple examples
are f(n)=0, f(n)=1, and f(n)=nc
(for a fixed positive value c).
If f(n) is multiplicative and we factor n into distinct primes as n=p1a1. p2a2. ....pkak, then f(n) = f(p1)a1. f(p2)a2. ....f(pk)ak.
Chris K. Caldwell © 1999-2013 (all rights reserved)
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