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Integers k such that omega(k) = omega(k-1) + omega(k-2) + omega(k-3), where omega(n) is the number of distinct prime factors of n.
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%I #21 Nov 22 2024 06:04:27

%S 2310,3990,4290,6090,6270,10010,11550,12810,13650,17094,17940,18270,

%T 19380,21930,22110,22770,23100,24990,25410,27300,28644,30090,32214,

%U 32604,34034,34314,35340,35880,37310,38190,38570,38640,39270,39780

%N Integers k such that omega(k) = omega(k-1) + omega(k-2) + omega(k-3), where omega(n) is the number of distinct prime factors of n.

%H Harvey P. Dale, <a href="/A076252/b076252.txt">Table of n, a(n) for n = 1..1000</a>

%e omega(2310) = 5 = 1 + 2 + 2 = omega(2309) + omega(2308) + omega(2307), so 2310 belongs to the sequence.

%t omega[n_] := Length[FactorInteger[n]]; a = {}; Do[If[omega[n] == omega[n - 1] + omega[n - 2] + omega[n - 3], a = Append[a, n]], {n, 1, 10^5}]; a

%t Flatten[Position[Partition[PrimeNu[Range[40000]],4,1],_?(#[[4]] == Total[ Take[ #,3]]&), {1}, Heads->False]]+3 (* _Harvey P. Dale_, Oct 31 2016 *)

%Y Cf. A001221, A006049, A076251, A076253.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Nov 04 2002