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A087978
a(n) is the first term in a chain of at least n consecutive numbers, each having exactly m = 5 distinct prime factors.
6
2310, 254540, 1042404, 21871365, 129963314, 830692265, 4617927894, 18297409143, 41268813542, 287980277114, 1182325618032, 6455097761454, 14207465691240, 54049709480208, 90987640183352, 546525829796442, 546525829796442
OFFSET
1,1
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]
MATHEMATICA
k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={5}, k++ ]; Print[k], {n, 1, 8}]
CROSSREFS
Cf. A064708 (m=2), A080569 (m=3), A087977 (m=4).
Cf. A138206, A138207, A154573. - Donovan Johnson, Jan 15 2009
Cf. A046387.
Sequence in context: A046303 A046403 A288072 * A384507 A261210 A020435
KEYWORD
nonn,fini,more
AUTHOR
Labos Elemer, Sep 26 2003
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
STATUS
approved