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A114455
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Numbers n such that the n-th hexagonal number is a 4-almost prime.
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1
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12, 23, 25, 26, 27, 30, 33, 35, 39, 42, 45, 46, 52, 53, 58, 59, 62, 65, 66, 70, 75, 76, 83, 85, 93, 94, 99, 111, 114, 117, 118, 119, 131, 133, 134, 137, 145, 146, 147, 154, 155, 161, 163, 167, 173, 174, 175, 178, 179, 183, 190, 193, 195, 202, 206, 209, 214, 219, 222, 226, 231, 233, 235, 237, 239
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OFFSET
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1,1
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COMMENTS
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There are no prime hexagonal numbers. The n-th Hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Hexagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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n such that hexagonal number A000384(n) is an element of A014613. n such that A001222(A000384(n)) = 4. n such that A001222(n*(2*n-1)) = 4.
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EXAMPLE
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a(1) = 12 because HexagonalNumber(12) = H(12) = 12*(2*12-1) = 276 = 2^2 * 3 * 23 is a 4-almost prime.
a(2) = 23 because H(23) = 23*(2*23-1) = 1035 = 3^2 * 5 * 23 is a 4-almost prime.
a(3) = 25 because H(25) = 25*(2*25-1) = 1225 = 5^2 * 7^2 is a 4-almost prime.
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MATHEMATICA
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Select[Range[250], PrimeOmega[#(2#-1)]==4&] (* Harvey P. Dale, Feb 18 2013 *)
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CROSSREFS
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Cf. A000384, A001222, A014613.
Sequence in context: A246342 A101104 A330212 * A048992 A088783 A029756
Adjacent sequences: A114452 A114453 A114454 * A114456 A114457 A114458
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Feb 14 2006
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EXTENSIONS
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40 removed by R. J. Mathar, Dec 22 2010
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STATUS
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approved
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