A215085 a(n) = (A214089(n)^2 - 1) divided by four times the product of the first n primes.

1, 1, 1, 1, 19, 17, 1, 2567, 3350, 128928, 3706896, 1290179, 100170428, 39080794, 61998759572, 7833495265, 45119290746, 581075656330, 8672770990, 15792702394898740, 594681417768520250, 25509154378676494, 1642780344643617537867, 480931910076867717575

Offset: 1

Author

J. Stauduhar, Aug 02 2012

Keywords

• nonn

Comments

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

Examples

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

Links

• J. Stauduhar, Table of n, a(n) for n = 1..30

Programs

Maple

A215085 := proc(n)
        (A214089(n)^2-1)/4/A002110(n) ;
end proc: # R. J. Mathar, Aug 21 2012

Python

from itertools import product
from sympy import sieve, prime, isprime, primorial
from sympy.ntheory.modular import crt
def A215085(n):
    return (
        1
        if n == 1
        else (
            int(
                min(
                    filter(
                        isprime,
                        (
                            crt(tuple(sieve.primerange(prime(n) + 1)), t)[0]
                            for t in product((1, -1), repeat=n)
                        ),
                    )
                )
            )
            ** 2
            - 1
        )
        // 4
        // primorial(n)
    )  # Chai Wah Wu, May 31 2022
for n in range(1, 16):
    print(A215085(n), end=", ")

Formula

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