加法的関数
ω(4) = 1 ω(20) = ω(2 ⋅ 5) = 2 ω(27) = 1 ω(144) = ω(2 ⋅ 3) = ω(2) + ω(3) = 1 + 1 = 2 ω(2000) = ω(2 ⋅ 5) = ω(2) + ω(5) = 1 + 1 = 2 ω(2001) = 3 ω(2002) = 4 ω(2003) = 1 ω(54032858972279) = 3 ω(54032858972302) = 5 ω(20802650704327415) = 5
a1(n): n の異なる素因数の和。sopf(n) とも呼ばれる(オンライン整数列大辞典の数列 A008472)。例:
a1(1) = 0 a1(4) = 2 a1(20) = 2 + 5 = 7 a1(27) = 3 a1(144) = a1(2 ⋅ 3) = a1(2) + a1(3) = 2 + 3 = 5 a1(2000) = a1(2 ⋅ 5) = a1(2) + a1(5) = 2 + 5 = 7 a1(2001) = 55 a1(2002) = 33 a1(2003) = 2003 a1(54032858972279) = 1238665 a1(54032858972302) = 1780410 a1(20802650704327415) = 1238677