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%I #14 Aug 29 2021 15:28:33
%S 1870,2090,2470,2530,2990,3190,3410,3458,3770,3910,4030,4070,4186,
%T 4510,4730,4810,4930,5170,5187,5270,5278,5330,5474,5510,5590,5642,
%U 5830,5890,6110,6279,6290,6490,6710,6734,6890,6902,6970,7030,7130,7310,7370,7378
%N Squarefree numbers having exactly three prime gaps.
%H Amiram Eldar, <a href="/A073489/b073489.txt">Table of n, a(n) for n = 1..10000</a>
%F A073484(a(n)) = 3.
%e 1870 is a term, as 1870 = 2*5*11*17 = with three gaps: between 2 and 5, between 5 and 11 and between 11 and 17.
%t q[n_] := SequenceCount[FactorInteger[n][[;; , 1]], {p1_, p2_} /; p2 != NextPrime[p1], Overlaps -> True] == 3; Select[Range[7500], SquareFreeQ[#] && q[#] &] (* _Amiram Eldar_, Apr 10 2021 *)
%t sfQ[n_]:=SquareFreeQ[n]&&Total[Boole[NextPrime[#[[1]]]!=#[[2]]&/@ Partition[ FactorInteger[n][[All,1]],2,1]]]==3; Select[Range[7500],sfQ] (* _Harvey P. Dale_, Aug 29 2021 *)
%Y Cf. A005117, A073484, A073486, A073488, A073495.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 03 2002