Revision as of 05:14, 19 January 2025 edit AWikipedian25 (talk \| contribs) 29 edits m →Ω(n), ω(n), νp(n) – prime power decomposition ← Previous edit		Revision as of 06:39, 24 January 2025 edit undo John Baez (talk \| contribs) Extended confirmed users 2,516 edits →Multiplicative and additive functions: fixed definitions of multiplicative and completely multiplicative arithmetic functions: we must require a(1) = 1, and the linked Wikipedia page points that out already. Next edit →
Line 11: An arithmetic function ''a'' is * '''[[Completely additive function\|completely additive]]''' if ''a''(''mn'') = ''a''(''m'') + ''a''(''n'') for all natural numbers ''m'' and ''n''; * '''[[Completely multiplicative function\|completely multiplicative]]''' if ''a''(1) = 1 and ''a''(''mn'') = ''a''(''m'')''a''(''n'') for all natural numbers ''m'' and ''n''; Two whole numbers ''m'' and ''n'' are called [[coprime]] if their [[greatest common divisor]] is 1, that is, if there is no [[prime number]] that divides both of them. Line 17: Then an arithmetic function ''a'' is * '''[[Additive function\|additive]]''' if ''a''(''mn'') = ''a''(''m'') + ''a''(''n'') for all coprime natural numbers ''m'' and ''n''; * '''[[Multiplicative function\|multiplicative]]''' if ''a''(1) = 1 and ''a''(''mn'') = ''a''(''m'')''a''(''n'') for all coprime natural numbers ''m'' and ''n''. == Notation ==

Arithmetic function: Difference between revisions