A358178 a(n) is the cardinality of the set of distinct pairwise gcd's of {1! + 1, ..., n! + 1}.

0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18

Offset: 1

Author

Gleb Ivanov, Nov 02 2022

Keywords

• nonn

Examples

			For n = 6 initial set is {1+1, 2+1, 6+1, 24+1, 120+1, 720+1} and after applying gcd for each distinct pair of elements we get {1, 7} set with cardinality of a(6) = 2.
		

Crossrefs

Cf. A038507, A358127, A356371, A214799.

Programs

Python

from math import gcd, factorial
from itertools import combinations
f, terms = [2,], []
for i in range(2,100):
    f.append(factorial(i)+1)
    terms.append(len(set([gcd(*t) for t in combinations(f, 2)])))
print(terms)

Python

from math import gcd
from itertools import count, islice
def A358178_gen(): # generator of terms
    m, f, g = 1, [], set()
    for n in count(1):
        m *= n
        g |= set(gcd(d,m+1) for d in f)
        f.append(m+1)
        yield len(g)
A358178_list = list(islice(A358178_gen(),20)) # Chai Wah Wu, Dec 15 2022