Class A000010

The integer sequence A000010 is Euler's totient function.

Number of positive integers $i < n$ that are relative prime to $n$.
Number of totatives of $n$.

Euler totient function $\phi(n)$: count numbers < $n$ and prime to $n$.
euler_phi is a standard SAGE function implemented in PARI


INPUT:
    n -- positive integer

OUTPUT:
    integer -- function value

EXAMPLES:
    sage: a = sloane.A000010; a
    Euler's totient function
    sage: a(1)
    1
    sage: a(0)
    Traceback (most recent call last):
    ...
    ValueError: input n (=0) must be a positive integer
    sage: a(11)
    10
    sage: a.list(12)
    [1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4]
    sage: a(1/3)
    Traceback (most recent call last):
    ...
    TypeError: input must be an int, long, or Integer

   
AUTHOR:
    -- Jaap Spies (2007-01-12)

Overrides: SloaneSequence.__init__

EXAMPLES:
    sage: sloane.A000010._repr_()
    "Euler's totient function"

Overrides: SloaneSequence._repr_