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A368589
Lesser of 2 successive squarefree semiprimes (k, k+5) sandwiching 4 consecutive nonsquarefree numbers.
0
3749, 13373, 16574, 20573, 21461, 24449, 51542, 63746, 64049, 79673, 79721, 107846, 110102, 134306, 149642, 155966, 161549, 184922, 201074, 201221, 212021, 228974, 244949, 259073, 270917, 282446, 282533, 283706, 283742, 284246, 295322, 319874, 328346, 343274
OFFSET
1,1
EXAMPLE
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.
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.
MATHEMATICA
Select[Partition[Select[Range[350000], SquareFreeQ], 2, 1], Differences[#] == {5} && PrimeOmega[#] == {2, 2} &][[;; , 1]] (* Amiram Eldar, Dec 31 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Massimo Kofler, Dec 31 2023
STATUS
approved