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%I #45 Sep 30 2022 16:30:08
%S 210,46189,667,1147,82861,3127,4087,409457,7387,97,121330189,113,127,
%T 2494633,149,23707,27221,30967,181,1445140189,1,211,11592209,55687,
%U 241,64507,70747,75067,79523,293,307,30857731,1,111547,121103,126727,367,141367,148987,397,164009,419,421
%N Product of the prime numbers that are between 10*n and 10*(n+1).
%C a(n) is prime iff n is in A216292. - _Amiram Eldar_, Aug 23 2022
%C For almost all n (in the sense of natural density), a(n) = 1. - _Charles R Greathouse IV_, Sep 30 2022
%F 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).
%F a(n) = 1 for n in A032352. - _Michel Marcus_, Aug 23 2022
%F a(n) = Product_{i=1+pi(10*n)..pi(10*(n+1))} prime(i). - _Alois P. Heinz_, Aug 23 2022
%e 210 = 2*3*5*7, 46189 = 11*13*17*19, 667 = 23*29, 1147 = 31*37, 82861 = 41*43*47.
%t a[n_] := Times @@ Select[Range[10 n + 1, 10 n + 9], PrimeQ]; Array[a, 43, 0]
%o (PARI) a(n) = vecprod(select(isprime, [10*n..10*(n+1)])); \\ _Michel Marcus_, Aug 24 2022
%o (Python)
%o from math import prod
%o from sympy import primerange
%o def a(n): return prod(primerange(10*n, 10*(n+1)))
%o print([a(n) for n in range(43)]) # _Michael S. Branicky_, Aug 23 2022
%o (Python)
%o from math import prod
%o from sympy import isprime
%o 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
%Y Cf. A000040, A000720, A032352, A179816, A216292.
%K nonn,easy
%O 0,1
%A _Hemjyoti Nath_, Aug 23 2022
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