A368117 a(n) = Product_{(s - 2)|n, s prime} s if n > 0, a(0) = 1.

1, 3, 3, 15, 3, 21, 15, 3, 3, 165, 21, 39, 15, 3, 3, 1785, 3, 57, 165, 3, 21, 345, 39, 3, 15, 21, 3, 4785, 3, 93, 1785, 3, 3, 195, 57, 777, 165, 3, 3, 615, 21, 129, 345, 3, 39, 922845, 3, 3, 15, 3, 21, 15105, 3, 3, 4785, 273, 3, 885, 93, 183, 1785, 3, 3

Offset: 0

Author

Peter Luschny, Dec 13 2023

Keywords

• nonn

Comments

All terms are squarefree.

Examples

			The divisors of 15 are {1, 3, 5, 15}. Adding 2 to the divisors gives {3, 5, 7, 17}, which are all primes. Therefore a(15) = 3*5*7*17 = 1785.
		

Crossrefs

Cf. A160014, A007947 (radical of n, m=0), A141056 and A027760 (Clausen numbers, m=1).

Programs

Mathematica

{1}~Join~Array[Times @@ Select[Divisors[#] + 2, PrimeQ] &, 62] (* Michael De Vlieger, Dec 14 2023 *)

PARI

a(n) = if (n>0, my(d=divisors(n)); prod(k=1, #d, if (isprime(p=d[k]+2), p, 1)), 1); \\ Michel Marcus, Dec 15 2023

SageMath

def a(n): return (mul(s for s in map(lambda i: i + 2, divisors(n))
                  if is_prime(s)) if n > 0 else 1)
print([a(n) for n in range(63)])

Formula

a(n) = A160014(2, n).