For example:::"a"0(4) = 2 + 2 = 4::"a"0(20) = "a"0(22 · 5) = 2 + 2+ 5 = 9::"a"0(27) = 3 + 3 + 3 = 9::"a"0(144) = "a"0(24 · 32) = "a"0(24) + "a"0(32) = 8 + 6 = 14::"a"0(2,000) = "a"0(24 · 53) = "a"0(24) + "a"0(53) = 8 + 15 = 23::"a"0(2,003) = 2003::"a"0(54,032,858,972,279) = 1240658::"a"0(54,032,858,972,302) = 1780417::"a"0(20,802,650,704,327,415) = 1240681* The function Ω("n"), defined as the total number of prime factors of "n", counting multiple factors multiple times, sometimes called the "Big Omega function" .
::"a"0(4) = 4::"a"0(27) = 9::"a"0(144) = "a"0(24 · 32) = "a"0(24) + "a"0(32) = 8 + 6 = 14::"a"0(2,000) = "a"0(24 · 53) = "a"0(24) + "a"0(53) = 8 + 15 = 23::"a"0(2,001) = 55::"a"0(2,002) = 33::"a"0(2,003) = 2003::"a"0(54,032,858,972,279) = 1240658::"a"0(54,032,858,972,302) = 1780417::"a"0(20,802,650,704,327,415) = 1240681* "a"1("n") - la somma dei primi distinti che dividono "n".