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%I #24 Jul 24 2023 10:18:42
%S 2310,254540,1042404,21871365,129963314,830692265,4617927894,
%T 18297409143,41268813542,287980277114,1182325618032,6455097761454
%N a(n) is the first term in a chain of at least n consecutive numbers, each having exactly m = 5 distinct prime factors.
%H Roger B. Eggleton and James A. MacDougall, <a href="http://www.jstor.org/stable/27643119">Consecutive integers with equally many principal divisors</a>, Math. Mag. 81 (2008), 235-248. [_T. D. Noe_, Oct 13 2008]
%H 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
%t k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={5}, k++ ]; Print[k], {n, 1, 8}]
%Y Cf. A064708 (m=2), A080569 (m=3), A087977 (m=4).
%Y Cf. A138206, A138207, A154573. - _Donovan Johnson_, Jan 15 2009
%K nonn,fini,more
%O 1,1
%A _Labos Elemer_, Sep 26 2003
%E More terms from _Don Reble_, Sep 29 2003
%E a(7)-a(10) from _Donovan Johnson_, Mar 06 2008
%E a(11)-a(12) from _Donovan Johnson_, Jan 15 2009
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