login
A215085
a(n) = (A214089(n)^2 - 1) divided by four times the product of the first n primes.
3
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
1,5
COMMENTS
When floor(A214089(n) / 2) = A118478(n), a(n) = A215021(n).
LINKS
FORMULA
a(n) = (A214089(n)^2 - 1) / (4 * A002110(n)).
EXAMPLE
A214089(14) = 1430083494841, n#_14 = 13082761331670030, and (1430083494841^2 - 1) / (4 * 13082761331670030) = 39080794, so a(14) = 39080794.
MAPLE
A215085 := proc(n)
(A214089(n)^2-1)/4/A002110(n) ;
end proc: # R. J. Mathar, Aug 21 2012
PROG
(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=", ")
CROSSREFS
Sequence in context: A269231 A135734 A215021 * A241525 A321332 A109410
KEYWORD
nonn
AUTHOR
J. Stauduhar, Aug 02 2012
STATUS
approved