Number Theory

n: positive integer

ISPRIME returns TRUE if n is prime and FALSE otherwise.

NT_D, NT_SIGMA.

i: positive integer

ITHPRIME finds the ith prime.

NT_D, NT_SIGMA.

n: positive integer

NT_D calculates the number of divisors of n.

ITHPRIME, NT_PHI, NT_SIGMA.

n: positive integer

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.

ITHPRIME, NT_PHI, NT_SIGMA, NT_D.

n: positive integer

Returns the number of distinct prime factors without multiplicity.

NT_D, ITHPRIME, NT_SIGMA.

n: positive integer

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

NT_D, ITHPRIME, NT_SIGMA.

n: positive integer

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

ITHPRIME, NT_PHI, NT_D, NT_SIGMA.

n: positive integer

The function computes the product of its distinct prime factors

NT_D, ITHPRIME, NT_SIGMA.

n: positive integer

NT_SIGMA calculates the sum of the divisors of n.

NT_D, ITHPRIME, NT_PHI.

n: positive integer

PFACTOR finds the smallest prime factor of its argument.

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

ITHPRIME.