cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A185042 #37 Jun 23 2025 10:03:26
%S A185042 210,7314,37960,134043,357642,2713332,1217250,14273478,44939642,
%T A185042 76067298,163459742,547163235,2081479430,2771263512,11715712410,
%U A185042 17911205580,56608713884,203594236366,118968284928,2500769994070,3157129230489,22498525938216,585927201062
%N A185042 Initial term of first run of exactly n consecutive numbers with 4 distinct prime factors.
%C A185042 The number of distinct prime factors is A001221.
%C A185042 a(23) = 585927201062; a(n) > 10^13 for n = 20, 21, 22, and n >= 24, if they exist.
%C A185042 Eggleton and MacDougall show that there are no more than 419 terms in this sequence.
%C A185042 a(28) > 2 * 10^15. - _Toshitaka Suzuki_, Jun 22 2025
%H A185042 Toshitaka Suzuki, <a href="/A185042/b185042.txt">Table of n, a(n) for n = 1..27</a>
%H A185042 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 A185042 Roger B. Eggleton, Jason S. Kimberley, and James 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 Newcastle’s Digital Research Repository (2009).
%e A185042 a(6) > a(7) because the first run of 6 consecutive integers i with A001221(i)=4 is not maximal.
%Y A185042 Cf. A064709, A185032, A087977.
%K A185042 nonn,fini
%O A185042 1,1
%A A185042 Roger B. Eggleton, _Jason Kimberley_, and James A. MacDougall, Apr 12 2011
%E A185042 a(20)-a(22) from and a(23) added by _Toshitaka Suzuki_, Mar 24 2025