A356690 Product of the prime numbers that are between 10*n and 10*(n+1).

210, 46189, 667, 1147, 82861, 3127, 4087, 409457, 7387, 97, 121330189, 113, 127, 2494633, 149, 23707, 27221, 30967, 181, 1445140189, 1, 211, 11592209, 55687, 241, 64507, 70747, 75067, 79523, 293, 307, 30857731, 1, 111547, 121103, 126727, 367, 141367, 148987, 397, 164009, 419, 421

Offset: 0

Author

Hemjyoti Nath, Aug 23 2022

Keywords

• nonn
• easy

Comments

a(n) is prime iff n is in A216292. - Amiram Eldar, Aug 23 2022

For almost all n (in the sense of natural density), a(n) = 1. - Charles R Greathouse IV, Sep 30 2022

Examples

			210 = 2*3*5*7, 46189 = 11*13*17*19, 667 = 23*29, 1147 = 31*37, 82861 = 41*43*47.
		

Crossrefs

Cf. A000040, A000720, A032352, A179816, A216292.

Programs

Mathematica

a[n_] := Times @@ Select[Range[10 n + 1, 10 n + 9], PrimeQ]; Array[a, 43, 0]

PARI

a(n) = vecprod(select(isprime, [10*n..10*(n+1)])); \\ Michel Marcus, Aug 24 2022

Python

from math import prod
from sympy import primerange
def a(n): return prod(primerange(10*n, 10*(n+1)))
print([a(n) for n in range(43)]) # Michael S. Branicky, Aug 23 2022

Python

from math import prod
from sympy import isprime
def A356690(n): return prod(m for i in (1,3,7,9) if isprime(m:=10*n+i)) if n else 210 # Chai Wah Wu, Sep 23 2022

Formula

Let m(n) = {isprime(10n-9) * (10n-9), isprime(10n-8) * (10n-8), isprime(10n-7) * (10n-7), isprime(10n-5) * (10n-5), isprime(10n-3) * (10n-3), isprime(10n-1) * (10n-1)}, where isprime = A010051; then a(n) = product of nonzero terms from m(n).

a(n) = 1 for n in A032352. - Michel Marcus, Aug 23 2022

a(n) = Product_{i=1+pi(10*n)..pi(10*(n+1))} prime(i). - Alois P. Heinz, Aug 23 2022