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 A185042 Initial term of first run of exactly n consecutive numbers with 4 distinct prime factors. 1

%I

%S 210,7314,37960,134043,357642,2713332,1217250,14273478,44939642,

%T 76067298,163459742,547163235,2081479430,2771263512,11715712410,

%U 17911205580,56608713884,203594236366,118968284928

%N Initial term of first run of exactly n consecutive numbers with 4 distinct prime factors.

%C The number of distinct prime factors is A001221.

%C a(23) = 585927201062; a(n) > 10^13 for n = 20, 21, 22, and n >= 24, if they exist.

%C Eggleton and MacDougall show that there are no more than 419 terms in this sequence.

%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.

%H R. B. Eggleton, J. S. Kimberley, and J. A. MacDougall, <a href="http://hdl.handle.net/1959.13/35886">Principal divisor ranks of the first trillion positive integers</a>, NOVA: The University of Newcastleâ€™s Digital Research Repository (2009).

%e a(6) > a(7) because the first run of 6 consecutive integers i with A001221(i)=4 is not maximal.

%Y Cf. A064709, A185032, and A087977.

%K nonn,fini,more

%O 1,1

%A R. B. Eggleton, _Jason Kimberley_, and J. A. MacDougall, Apr 12 2011

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Last modified September 27 09:09 EDT 2020. Contains 337380 sequences. (Running on oeis4.)