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%I #7 Jan 25 2024 07:15:33
%S 3749,13373,16574,20573,21461,24449,51542,63746,64049,79673,79721,
%T 107846,110102,134306,149642,155966,161549,184922,201074,201221,
%U 212021,228974,244949,259073,270917,282446,282533,283706,283742,284246,295322,319874,328346,343274
%N Lesser of 2 successive squarefree semiprimes (k, k+5) sandwiching 4 consecutive nonsquarefree numbers.
%e 3749 = 23 * 163 and 3754 = 2 * 1877 are squarefree semiprime; 3750 = 2 * 3 * 5^4, 3751 = 11^2 * 31, 3752 = 2^3 * 7 * 67 and 3753 = 3^3 * 139 are 4 consecutive nonsquarefree numbers, so 3749 is a term.
%e 13373 = 43 * 311 and 13378 = 2 * 6689 are squarefree semiprime; 13374 = 2 * 3^2 * 743, 13375 = 5^3 * 107, 13376 = 2^6 * 11 * 19 and 13377 = 3 * 7^3 * 13 are 4 consecutive nonsquarefree numbers, so 13373 is a term.
%t Select[Partition[Select[Range[350000], SquareFreeQ], 2, 1], Differences[#] == {5} && PrimeOmega[#] == {2, 2} &][[;; , 1]] (* _Amiram Eldar_, Dec 31 2023 *)
%Y Cf. A006881, A013929, A363821.
%K nonn
%O 1,1
%A _Massimo Kofler_, Dec 31 2023