OFFSET
1,3
COMMENTS
By definition of A276710, a(n) >= -1.
It is conjectured that a(n) >= 0, computationally verified up to n = 10^7.
Empirically from terms up to n=10^7, a(n) seems to become quite large, small values are rare, and yet a(n)=0 also seems to occur for large n.
EXAMPLE
The 7th term of A276710 is 105 because Product_{k=1..105} binomial(36,k) is divisible by 105^(105-1). Actually, it is divisible by 105^(105+49), but not by 105^(105+50). Therefore, a(7) = 49.
PROG
(Python)
from math import prod, comb
from itertools import islice
from sympy import nextprime
def A353010_gen(): # generator of terms
p, q = 3, 5
while True:
for m in range(p+1, q):
r = m**(m-1)
c = 1
for k in range(m+1):
c = c*comb(m, k) % r
if c == 0:
d, (e, f) = -m, divmod(prod(comb(m, k) for k in range(m+1)), m)
while f == 0:
d += 1
e, f = divmod(e, m)
yield d
p, q = q, nextprime(q)
CROSSREFS
KEYWORD
nonn
AUTHOR
Hagen von Eitzen, Apr 15 2022
STATUS
approved