Number Theory

ISPRIME

ISPRIME whether n is prime

Synopsis

ISPRIME(n)

Arguments

n: positive integer

Description

ISPRIME returns TRUE if n is prime and FALSE otherwise.

See also

NT_D, NT_SIGMA.

ITHPRIME

ITHPRIME ith prime

Synopsis

ITHPRIME(i)

Arguments

i: positive integer

Description

ITHPRIME finds the ith prime.

See also

NT_D, NT_SIGMA.

NT_D

NT_D number of divisors

Synopsis

NT_D(n)

Arguments

n: positive integer

Description

NT_D calculates the number of divisors of n.

See also

ITHPRIME, NT_PHI, NT_SIGMA.

NT_MU

NT_MU Möbius mu function

Synopsis

NT_MU(n)

Arguments

n: positive integer

Description

NT_MU function (Möbius mu function) returns 0 if n is divisible by the square of a prime. Otherwise, if n has an odd number of different prime factors, NT_MU returns -1, and if n has an even number of different prime factors, it returns 1. If n = 1, NT_MU returns 1.

See also

ITHPRIME, NT_PHI, NT_SIGMA, NT_D.

NT_OMEGA

NT_OMEGA Number of distinct prime factors

Synopsis

NT_OMEGA(n)

Arguments

n: positive integer

Note

Returns the number of distinct prime factors without multiplicity.

See also

NT_D, ITHPRIME, NT_SIGMA.

NT_PHI

NT_PHI Euler's totient function

Synopsis

NT_PHI(n)

Arguments

n: positive integer

Note

Euler's totient function gives the number of integers less than or equal to n that are relatively prime (coprime) to n.

See also

NT_D, ITHPRIME, NT_SIGMA.

NT_PI

NT_PI number of primes upto n

Synopsis

NT_PI(n)

Arguments

n: positive integer

Description

NT_PI returns the number of primes less than or equal to n.

See also

ITHPRIME, NT_PHI, NT_D, NT_SIGMA.

NT_SIGMA

NT_SIGMA sigma function

Synopsis

NT_SIGMA(n)

Arguments

n: positive integer

Description

NT_SIGMA calculates the sum of the divisors of n.

See also

NT_D, ITHPRIME, NT_PHI.

PFACTOR

PFACTOR smallest prime factor

Synopsis

PFACTOR(n)

Arguments

n: positive integer

Description

PFACTOR finds the smallest prime factor of its argument.

Note

The argument n must be at least 2. Otherwise a #VALUE! error is returned.

See also

ITHPRIME.