cp's OEIS Frontend

A325480 a(n) is the largest integer m such that the product of n consecutive integers starting at m is divisible by at most n primes.

%I A325480 #26 Nov 20 2023 00:03:10
%S A325480 16,24,24,45,48,49,120,120,125,189,240,240,350,350,350,350,374,494,
%T A325480 494,714,714,714,714,825,832,1078,1078,1078,1078,1425,1440,1440,1856,
%U A325480 2175,2175,2175,2175,2175,2175,2175,2870,2870,2870,2871,2880,2880,2880,3219
%N A325480 a(n) is the largest integer m such that the product of n consecutive integers starting at m is divisible by at most n primes.
%C A325480 Each term is only conjectured and has been verified up to 10^6.
%C A325480 Note a(2) is undefined if there are infinitely many Mersenne primes.
%e A325480 For example, a(3) = 16 because 16 * 17 * 18 = 2^5 * 3^2 * 17 admits only three prime divisors (2, 3, and 17) and appears to be the largest product of three consecutive integers with the property.
%o A325480 (SageMath)
%o A325480 for r in range(3, 100):
%o A325480   history = []
%o A325480   M = 0
%o A325480   for n in range(1, 100000):
%o A325480     primes = {p for p, _ in factor(n)}
%o A325480     history.append(primes)
%o A325480     history = history[-r:]
%o A325480     total = set()
%o A325480     for s in history: total |= s
%o A325480     # Skip if too many primes.
%o A325480     if len(total) > r: continue
%o A325480     if n > M: M = n
%o A325480   print(r, M-r+1)
%Y A325480 Cf. A002182, A045619, A163264, A164799, A239035, A244656, A006549.
%K A325480 nonn
%O A325480 3,1
%A A325480 _Onno M. Cain_, Sep 06 2019