A087978 a(n) is the first term in a chain of at least n consecutive numbers, each having exactly m = 5 distinct prime factors.

2310, 254540, 1042404, 21871365, 129963314, 830692265, 4617927894, 18297409143, 41268813542, 287980277114, 1182325618032, 6455097761454, 14207465691240, 54049709480208, 90987640183352, 546525829796442, 546525829796442

Offset: 1

Author

Labos Elemer, Sep 26 2003

Keywords

• nonn
• fini
• more

Comments

Every chain of 30030 consecutive numbers has exactly one number divisible by 30030 = 2 * 3 * 5 * 7 * 11 * 13 hence is divisible by more than five distinct primes. Therefore the sequence is finite. - David A. Corneth, Jul 19 2023

a(18) > 2 * 10^15. - Toshitaka Suzuki, Jun 23 2025

Links

• Roger B. Eggleton and James A. MacDougall, Consecutive Integers with Equally Many Principal Divisors, Math. Mag. 81 (2008), 235-248. [_T. D. Noe_, Oct 13 2008]

Crossrefs

Cf. A064708 (m=2), A080569 (m=3), A087977 (m=4).

Cf. A138206, A138207, A154573. - Donovan Johnson, Jan 15 2009

Cf. A046387.

Programs

Mathematica

k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={5}, k++ ]; Print[k], {n, 1, 8}]

Extensions

More terms from Don Reble, Sep 29 2003

a(7)-a(10) from Donovan Johnson, Mar 06 2008

a(11)-a(12) from Donovan Johnson, Jan 15 2009

a(13)-a(15) from Toshitaka Suzuki, Apr 06 2025

a(16)-a(17) from Toshitaka Suzuki, Jun 23 2025