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Totient ​

Euler's totient function: the count of integers in 1..n coprime to n.

WikipediaEuler's totient functionMathWorldTotientFunctionWikidataQ190026Encyclopedia of MathematicsEuler_functionBritannicatopic/Euler-phi-functionDLMF27.2.E7FungrimTotient✓Fungrim entryOEISA000010Wolfram LanguageEulerPhi✓
Totient(n)count of integers in coprime to , Euler's .
SageMatheuler_phi(n)SymPytotient(n)

Domain: Number theory

Details
  • Also called Euler's phi function; central to RSA key generation and elementary number theory.
  • Multiplicative: whenever .
  • For , .
  • Divisor sum identity: .
  • compute-engine requires a positive integer.

Examples

See also: MultiplicativeOrder, DivisorSigma