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%I #12 Nov 22 2023 22:15:39
%S 602,1374,2274,2522,3122,3282,4202,4922,4958,4974,5822,5885,6874,7298,
%T 7674,9062,9422,9474,10322,11222,12590,13074,15531,15722,16818,18766,
%U 19131,19745,20447,21535,22922,24774,24938,25323,25622,26522,26738,27978,28034,28074,28222
%N Lesser of 2 successive sphenic numbers (k, k+4) sandwiching 3 consecutive nonsquarefree numbers.
%e 602 = 2 * 7 * 43 and 606 = 2 * 3 * 101 are sphenic numbers; 603 = 3^2 * 67, 604 = 2^2 * 151 and 605 = 5 * 11^2 are 3 consecutive nonsquarefree numbers, so 602 is a term.
%e 1374 = 2 * 3 * 229 and 1378 = 2 * 13 * 53 are sphenic numbers; 1375 = 5^3 * 11, 1376 = 2^5 * 43 and 1377 = 3^4 * 17 are 3 consecutive nonsquarefree numbers, so 1374 is a term.
%t Select[Partition[Select[Range[30000], FactorInteger[#][[;; , 2]] == {1, 1, 1} &], 2, 1], Differences[#] == {4} && ! Or @@ SquareFreeQ /@ Range[First[#] + 1, Last[#] - 1] &][[;; , 1]] (* _Amiram Eldar_, Oct 19 2023 *)
%Y Cf. A007304, A013929.
%K nonn
%O 1,1
%A _Massimo Kofler_, Oct 19 2023