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A114456
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Numbers n such that the n-th hexagonal number is a 5-almost prime.
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1
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8, 14, 16, 18, 20, 24, 28, 36, 38, 40, 41, 44, 54, 74, 77, 78, 84, 86, 90, 92, 100, 102, 105, 110, 113, 123, 124, 125, 126, 130, 132, 135, 136, 143, 148, 149, 153, 156, 164, 165, 170, 171, 184, 185, 186, 194, 207, 210, 213, 215, 218, 220, 225, 232, 234, 236
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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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FORMULA
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EXAMPLE
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a(1) = 8 because HexagonalNumber(8) = H(8) = 8*(2*8-1) = 120 = 2^3 * 3 * 5 is a 5-almost prime.
a(2) = 14 because H(14) = 14*(2*14-1) = 378 = 2 * 3^3 * 7 is a 5-almost prime.
a(3) = 18 because H(18) = 18*(2*18-1) = 630 = 2 * 3^2 * 5 * 7 is a 5-almost prime.
a(20) = 100 because H(100) = 100*(2*100-1) = 19900 = 2^2 * 5^2 * 199 is a 5-almost prime.
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MATHEMATICA
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Select[Range[300], PrimeOmega[#*(2*# - 1)] == 5 &] (* Giovanni Resta, Jun 14 2016 *)
Select[Range[300], PrimeOmega[PolygonalNumber[6, #]]==5&] (* Harvey P. Dale, Jan 15 2023 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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