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

3,1

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.

Links

Table of n, a(n) for n=3..50.

Example

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.

Prog

(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)

Crossrefs

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

Sequence in context: A114405 A098351 A206267 * A205193 A052058 A105732

Adjacent sequences: A325477 A325478 A325479 * A325481 A325482 A325483

Keyword

nonn

Author

Onno M. Cain, Sep 06 2019

Status

approved