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%I #5 Jul 22 2023 17:03:58
%S 186,266,322,470,518,534,582,590,670,754,790,814,894,994,1146,1158,
%T 1166,1338,1390,1562,1686,1798,1842,1958,2118,2158,2230,2318,2454,
%U 2482,2514,2570,2630,2758,2786,2922,2930,2994,3154,3206,3262,3278,3378,3454,3522,3562,3714,3786,3830,3838,3962,3982
%N Sphenic numbers sandwiched between two squarefree semiprimes.
%C Sphenic numbers are numbers that are products of three distinct primes.
%C This sequence is different from A362811: sphenic numbers sandwiched between semiprimes, as semiprimes are products of two primes that might not be distinct.
%e 186 = 2*3*31 is a sphenic number sandwiched between 185 = 5*37 and 187 = 11*17, both of which are squarefree semiprimes. Thus, 186 is in this sequence.
%e 290 = 2*5*29 is a sphenic number sandwiched between semiprimes 289 = 17*17 and 291 = 3*97, one of which is not squarefree. Thus, 290 is not in this sequence but in A362811.
%t Select[Range[4000], Transpose[FactorInteger[#]][[2]] == {1, 1, 1} && Transpose[FactorInteger[# - 1]][[2]] == {1, 1} && Transpose[FactorInteger[# + 1]][[2]] == {1, 1} &]
%Y Cf. A006881, A007304, A362811
%K nonn
%O 1,1
%A _Tanya Khovanova_ and _Massimo Kofler_, Jun 14 2023