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%I #29 Jul 11 2018 06:40:37
%S 210,7314,37960,134043,357642,1217250,1217250,14273478,44939642,
%T 76067298,163459742,547163235,2081479430,2771263512,11715712410,
%U 17911205580,56608713884,118968284928,118968284928,585927201062
%N a(n) is the first term in the first chain of at least n consecutive numbers each having exactly four distinct prime factors.
%C Eggleton and MacDougall show that there are no more than 419 terms in this sequence. - _T. D. Noe_, Oct 13 2008
%C a(24) > 10^13. - _Donovan Johnson_, Jan 15 2009
%H Donovan Johnson, <a href="/A087977/b087977.txt">Table of n, a(n) for n = 1..23</a>
%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.
%e a(6) = a(7) = 1217250 because the relevant 7 successive numbers have 4 distinct prime factors:
%e 1217250 = 2 * 3^2 * 5^3 * 541;
%e 1217251 = 7 * 17 * 53 * 193;
%e 1217252 = 2^2 * 23 * 101 * 131;
%e 1217253 = 3 * 47 * 89 * 97;
%e 1217254 = 2 * 19 * 103 * 311;
%e 1217255 = 5 * 13 * 61 * 307;
%e 1217256 = 2^3 * 3 * 67 * 757.
%t k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={4}, k++ ]; Print[k], {n, 1, 8}]
%t Module[{d4=Table[If[PrimeNu[n]==4,1,0],{n,143*10^5}]},Flatten[Table[ SequencePosition[d4,PadRight[{},n,1],1],{n,8}],1][[All,1]]] (* Requires Mathematica version 10 or later *) (* This generates the first 8 terms of the sequence *) (* _Harvey P. Dale_, Aug 25 2017 *)
%Y Cf. A080569 (m=3), A064708 (m=2).
%Y Cf. A087978, A138206, A138207, A154573.
%K nonn,fini
%O 1,1
%A _Labos Elemer_, Sep 26 2003
%E More terms from _Don Reble_, Sep 29 2003
%E a(13)-a(19) from _Donovan Johnson_, Mar 06 2008
%E a(20)-a(23) from _Donovan Johnson_, Jan 15 2009
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