Euler's Totient Function

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Euler's totient function (also known as the "phi function") counts the number of natural integers less than n that are coprime to n. It is very useful in number theory, e.g. to compute the number of primitive roots modulo a prime n. For more information, see:

• Wikipedia
• Encyclopedia of Mathematics
• Lindsay N. Childs, A Concrete Introduction to Higher Algebra, 3rd ed., Springer, 2009, pp. 111 and 179-180.
• G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, 6th ed., Oxford University Press, 2008, pp. 63-65.

The values presented below were computed in 2015 using a Python program.

• n = 1..1000
• n = 1001..2000
• n = 2001..3000
• n = 3001..4000
• n = 4001..5000
• n = 5001..6000
• n = 6001..7000
• n = 7001..8000
• n = 8001..9000
• n = 9001..10000
• n = 10001..11000
• n = 11001..12000
• n = 12001..13000
• n = 13001..14000
• n = 14001..15000
• n = 15001..16000
• n = 16001..17000
• n = 17001..18000
• n = 18001..19000
• n = 19001..20000
• n = 20001..21000
• n = 21001..22000
• n = 22001..23000
• n = 23001..24000
• n = 24001..25000
• n = 25001..26000
• n = 26001..27000
• n = 27001..28000
• n = 28001..29000
• n = 29001..30000
• n = 30001..31000
• n = 31001..32000
• n = 32001..33000
• n = 33001..34000
• n = 34001..35000
• n = 35001..36000
• n = 36001..37000
• n = 37001..38000
• n = 38001..39000
• n = 39001..40000
• n = 40001..41000
• n = 41001..42000
• n = 42001..43000
• n = 43001..44000
• n = 44001..45000
• n = 45001..46000
• n = 46001..47000
• n = 47001..48000
• n = 48001..49000
• n = 49001..50000
• n = 50001..51000
• n = 51001..52000
• n = 52001..53000
• n = 53001..54000
• n = 54001..55000
• n = 55001..56000
• n = 56001..57000
• n = 57001..58000
• n = 58001..59000
• n = 59001..60000
• n = 60001..61000
• n = 61001..62000
• n = 62001..63000
• n = 63001..64000
• n = 64001..65000
• n = 65001..66000
• n = 66001..67000
• n = 67001..68000
• n = 68001..69000
• n = 69001..70000
• n = 70001..71000
• n = 71001..72000
• n = 72001..73000
• n = 73001..74000
• n = 74001..75000
• n = 75001..76000
• n = 76001..77000
• n = 77001..78000
• n = 78001..79000
• n = 79001..80000
• n = 80001..81000
• n = 81001..82000
• n = 82001..83000
• n = 83001..84000
• n = 84001..85000
• n = 85001..86000
• n = 86001..87000
• n = 87001..88000
• n = 88001..89000
• n = 89001..90000
• n = 90001..91000
• n = 91001..92000
• n = 92001..93000
• n = 93001..94000
• n = 94001..95000
• n = 95001..96000
• n = 96001..97000
• n = 97001..98000
• n = 98001..99000
• n = 99001..100000

J.P. Martin-Flatin