A358178 - OEIS

%I #16 Dec 16 2022 09:00:57

%S 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,

%T 10,11,12,12,12,13,14,14,15,15,15,15,16,16,16,16,16,17,17,17,17,17,17,

%U 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

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

%e 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.

%o (Python)

%o from math import gcd, factorial

%o from itertools import combinations

%o f, terms = [2,], []

%o for i in range(2,100):

%o     f.append(factorial(i)+1)

%o     terms.append(len(set([gcd(*t) for t in combinations(f, 2)])))

%o print(terms)

%o (Python)

%o from math import gcd

%o from itertools import count, islice

%o def A358178_gen(): # generator of terms

%o     m, f, g = 1, [], set()

%o     for n in count(1):

%o         m *= n

%o         g |= set(gcd(d,m+1) for d in f)

%o         f.append(m+1)

%o         yield len(g)

%o A358178_list = list(islice(A358178_gen(),20)) # _Chai Wah Wu_, Dec 15 2022

%Y Cf. A038507, A358127, A356371, A214799.

%K nonn

%O 1,6

%A _Gleb Ivanov_, Nov 02 2022