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Numbers n such that n through n+5 have the same number of distinct prime factors.
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%I #26 Oct 26 2019 03:08:22

%S 91,141,142,143,212,213,214,323,324,2302,2303,6850,9061,10280,10281,

%T 15740,16130,16164,16682,16683,19052,19053,20212,20213,21195,21196,

%U 21790,22055,23064,25779,25780,25991,28608,28674,29971,31442,33084

%N Numbers n such that n through n+5 have the same number of distinct prime factors.

%H Amiram Eldar, <a href="/A045934/b045934.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2620 from Zak Seidov)

%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 The numbers from 91 to 96 all have 2 distinct prime factors: 91=7*13, 92=2^2*23, 93=3*31, 94=2*47, 95=5*19, and 96=2^5*3.

%t Select[Range[35000],Length[Union[Length/@FactorInteger[Range[#,#+5]]]]==1&] (* _Harvey P. Dale_, Feb 27 2011 *)

%Y Cf. A001221, A006049, A006073, A045932-A045933, A045935-A045938, A088983.

%K nonn

%O 1,1

%A _David W. Wilson_