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.

16, 24, 24, 45, 48, 49, 120, 120, 125, 189, 240, 240, 350, 350, 350, 350, 374, 494, 494, 714, 714, 714, 714, 825, 832, 1078, 1078, 1078, 1078, 1425, 1440, 1440, 1856, 2175, 2175, 2175, 2175, 2175, 2175, 2175, 2870, 2870, 2870, 2871, 2880, 2880, 2880, 3219

Offset: 3

Author

Onno M. Cain, Sep 06 2019

Keywords

• nonn

Comments

Each term is only conjectured and has been verified up to 10^6.

Note a(2) is undefined if there are infinitely many Mersenne primes.

Examples

			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.
		

Crossrefs

Cf. A002182, A045619, A163264, A164799, A239035, A244656, A006549.

Programs

SageMath

for r in range(3, 100):
  history = []
  M = 0
  for n in range(1, 100000):
    primes = {p for p, _ in factor(n)}
    history.append(primes)
    history = history[-r:]
    total = set()
    for s in history: total |= s
    # Skip if too many primes.
    if len(total) > r: continue
    if n > M: M = n
  print(r, M-r+1)