A334085 GCD of n and the product of all primes < n.

1, 1, 1, 2, 1, 6, 1, 2, 3, 10, 1, 6, 1, 14, 15, 2, 1, 6, 1, 10, 21, 22, 1, 6, 5, 26, 3, 14, 1, 30, 1, 2, 33, 34, 35, 6, 1, 38, 39, 10, 1, 42, 1, 22, 15, 46, 1, 6, 7, 10, 51, 26, 1, 6, 55, 14, 57, 58, 1, 30, 1, 62, 21, 2, 65, 66, 1, 34, 69, 70, 1, 6, 1, 74, 15

Offset: 1

Author

Christoph Schreier, Apr 14 2020

Keywords

• nonn
• easy

Comments

a(n) = 1 iff n is prime or n = 1.

Examples

			For n=8 the product of all primes < 8 = A034386(7) = 210; gcd(8,210) = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Christoph Schreier)

Crossrefs

Cf. A000040, A034386, A007947.

Programs

Maple

a:= n-> `if`(isprime(n), 1, mul(i[1], i=ifactors(n)[2])):
seq(a(n), n=1..80);  # Alois P. Heinz, Apr 17 2020

Mathematica

a[n_] := GCD[n, Times @@ Select[Range[n - 1], PrimeQ]]; Array[a, 60] (* Amiram Eldar, Apr 14 2020 *)

PARI

a(n) = gcd(n, prod(k=1, n-1, if (isprime(k), k, 1))); \\ Michel Marcus, Apr 14 2020

PARI

a(n,f=factor(n))=if(f[,2]==[1]~,1,factorback(f[,1])) \\ Charles R Greathouse IV, Apr 14 2020

Python

def is_prime(n):
    if n == 2 or n == 3:
        return True
    if n % 2 == 0 or n < 2:
        return False
    for i in range(3,int(n**0.5)+1,2):
        if n % i == 0:
            return False
    return True
def A(n):
    if n < 3:
        raise ValueError('n must be > 2')
    else:
        a = 1
        for i in range(n):
            if is_prime(i):
                a *= i
    return math.gcd(n,a)

Formula

a(n) = gcd(n, A034386(n-1)).

a(n) = 1 if n is prime, else a(n) = A007947(n).