A380937 Achilles numbers sandwiched between two semiprimes.
288, 392, 1944, 4500, 4608, 7200, 9248, 13068, 14112, 14792, 16200, 18000, 19652, 21632, 26136, 26912, 28800, 31104, 32000, 34992, 38088, 38988, 41472, 42592, 45000, 48668, 49000, 52272, 55112, 56448, 60552, 69984, 78732, 79092, 87808, 88200, 95832, 98568
Offset: 1
Keywords
Examples
288 = 2^5 * 3^2 (between 287 = 7 * 41 and 289 = 17^2). 392 = 2^3 * 7^2 (between 391 = 17 * 23 and 393 = 3 * 131). 1944 = 2^3 * 3^5 (between 1943 = 29 * 67 and 1945 = 5 * 389).
Programs
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Mathematica
achQ[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Min[e] > 1 && GCD @@ e == 1]; semiQ[n_] := PrimeOmega[n] == 2; Select[4*Range[25000], achQ[#] && And @@ semiQ /@ (# + {-1, 1}) &] (* Amiram Eldar, Apr 12 2025 *)
Comments