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a(n) = (A214089(n)^2 - 1) divided by four times the product of the first n primes.
3

%I #40 Jul 14 2024 08:42:50

%S 1,1,1,1,19,17,1,2567,3350,128928,3706896,1290179,100170428,39080794,

%T 61998759572,7833495265,45119290746,581075656330,8672770990,

%U 15792702394898740,594681417768520250,25509154378676494,1642780344643617537867,480931910076867717575

%N a(n) = (A214089(n)^2 - 1) divided by four times the product of the first n primes.

%C When floor(A214089(n) / 2) = A118478(n), a(n) = A215021(n).

%H J. Stauduhar, <a href="/A215085/b215085.txt">Table of n, a(n) for n = 1..30</a>

%F a(n) = (A214089(n)^2 - 1) / (4 * A002110(n)).

%e A214089(14) = 1430083494841, n#_14 = 13082761331670030, and (1430083494841^2 - 1) / (4 * 13082761331670030) = 39080794, so a(14) = 39080794.

%p A215085 := proc(n)

%p (A214089(n)^2-1)/4/A002110(n) ;

%p end proc: # _R. J. Mathar_, Aug 21 2012

%o (Python)

%o from itertools import product

%o from sympy import sieve, prime, isprime, primorial

%o from sympy.ntheory.modular import crt

%o def A215085(n):

%o return (

%o 1

%o if n == 1

%o else (

%o int(

%o min(

%o filter(

%o isprime,

%o (

%o crt(tuple(sieve.primerange(prime(n) + 1)), t)[0]

%o for t in product((1, -1), repeat=n)

%o ),

%o )

%o )

%o )

%o ** 2

%o - 1

%o )

%o // 4

%o // primorial(n)

%o ) # _Chai Wah Wu_, May 31 2022

%o for n in range(1, 16):

%o print(A215085(n), end=", ")

%K nonn

%O 1,5

%A _J. Stauduhar_, Aug 02 2012