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A371602
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Taxicab numbers that are sandwiched between squarefree numbers.
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2
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4104, 32832, 39312, 110808, 171288, 262656, 314496, 373464, 513000, 886464, 1016496, 1075032, 1195112, 1331064, 1370304, 1407672, 1609272, 1728216, 1734264, 1774656, 2101248, 2515968, 2864288, 2987712, 2991816, 3511872, 3512808, 3551112, 4104000, 4342914, 4467528, 4511808, 4607064
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OFFSET
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1,1
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COMMENTS
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All terms are even numbers.
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LINKS
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Christian Boyer, Les nombres Taxicabs, in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.
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EXAMPLE
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4104 = 2^3 * 3^3 * 19 (between 4103 = 11 * 373 and 4105 = 5 * 821).
32832 = 2^6 * 3^3 *19 (between 32831 and 32833, which are twin primes).
39312 = 2^4 * 3^3 * 7 * 13 (between 39311 = 19 * 2069 and 39313, which is prime).
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MATHEMATICA
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Select[Range[300000], And @@ SquareFreeQ /@ (# + {-1, 1}) && Length[PowersRepresentations[#, 2, 3]] > 1 &] (* Amiram Eldar, Mar 29 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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