A330349 a(n) = A070826(n+1) - 2^(n-1).

2, 13, 101, 1147, 14999, 255223, 4849781, 111546307, 3234846359, 100280244553, 3710369066381, 152125131761557, 6541380665830919, 307444891294237513, 16294579238595005981, 961380175077106286767

Offset

1,1

Comments

Conjecture: For each value of n, the power of each prime number in the prime factorization of a(n) is equal to 1.

Links

Table of n, a(n) for n=1..16.

Example

a(4) = 1147 = 31*37.
a(10) = A070826(11) - 2^9 = 100280245065 - 512 = 100280244553 = A000040(4129119109).

Prog

(PARI) a(n) = prod(k=1, n+1, prime(k))/2  - 2^(n-1); \\ Michel Marcus, Dec 11 2019
(Python)
from sympy import primorial
def A330349(n): return (primorial(n+1)>>1)-(1<<n-1) # Chai Wah Wu, Jul 21 2022

Crossrefs

Cf. A000040, A070826.

Sequence in context: A187746 A030519 A141116 * A234299 A301355 A077246

Adjacent sequences: A330346 A330347 A330348 * A330350 A330351 A330352

Keyword

nonn

Author

Ahmad J. Masad, Dec 11 2019

Status

approved