Totient Summatory Function

Φ(n) ≈ 3n²/π²

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n (1–500)

Φ(20) = Σφ(k)

128

3n²/π²: 121.6

|F_n|: 129

φ(k) & Φ(k)

k=1φ=1Φ=1

k=2φ=1Φ=2

k=3φ=2Φ=4

k=4φ=2Φ=6

k=5φ=4Φ=10

k=6φ=2Φ=12

k=7φ=6Φ=18

k=8φ=4Φ=22

k=9φ=6Φ=28

k=10φ=4Φ=32

k=11φ=10Φ=42

k=12φ=4Φ=46

k=13φ=12Φ=58

k=14φ=6Φ=64

k=15φ=8Φ=72

k=16φ=8Φ=80

k=17φ=16Φ=96

k=18φ=6Φ=102

k=19φ=18Φ=120

k=20φ=8Φ=128

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About Totient Summatory Function

A totient summatory function calculator computing Φ(n) = Σ_{k=1}^{n} φ(k). This counts the number of Farey fractions of order n, and Φ(n) ≈ 3n²/π². Shows cumulative totient values and the connection to the fraction count. Client-side.

Totient Summatory Function Features

Cumulative sum
φ(k) values
Asymptotic
Farey count
Graph

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