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A350284
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Numbers k which are the product of a cube greater than 1 and a prime, and where k-1 and k-2 are semiprimes.
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0
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16, 40, 88, 135, 328, 448, 1048, 1384, 1715, 1984, 2104, 2560, 2943, 3064, 3904, 4288, 5184, 5319, 6507, 6939, 7000, 7263, 7864, 8728, 9099, 9288, 9664, 11043, 11367, 12288, 15579, 17496, 17944, 18808, 22599, 23488, 24875, 25083, 25407, 26008, 26584, 30184, 30904, 31288, 31944
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OFFSET
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1,1
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COMMENTS
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Since there are an infinite number of semiprimes, there may be an infinite number of such numbers k. k=16 appears to be the only solution where the prime is 2.
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LINKS
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Table of n, a(n) for n=1..45.
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EXAMPLE
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k=16 is a term: 16 = 2^3 * 2, 15 = 3*5, and 14 = 2*7.
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MATHEMATICA
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q[n_] := ! PrimeQ[n] && Plus @@ Mod[FactorInteger[n][[;; , 2]], 3] == 1 && PrimeOmega[{n - 2, n - 1}] == {2, 2}; Select[Range[32000], q] (* Amiram Eldar, Dec 28 2021 *)
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PROG
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(PARI) isok(n)=my(s=factor(n)[, 2]~); select(e->e<>0, s%3)==[1] && s<>[1] && bigomega(n-1)==2 && bigomega(n-2)==2 \\ Andrew Howroyd, Dec 24 2021
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CROSSREFS
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Cf. A000578 (cubes), A001358 (semiprimes).
Sequence in context: A258258 A086046 A184030 * A182461 A205065 A185790
Adjacent sequences: A350281 A350282 A350283 * A350285 A350286 A350287
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KEYWORD
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nonn
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AUTHOR
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Sheldon Collier, Dec 23 2021
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STATUS
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approved
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