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Search: id:A114456
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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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| 8, 14, 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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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 A014614. n such that A001222(A000384(n)) = 5. n such that A001222(n*(2*n-1)) = 5.
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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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CROSSREFS
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Cf. A000384, A001222, A014614.
Sequence in context: A103338 A050681 A084021 this_sequence A138666 A072835 A096229
Adjacent sequences: A114453 A114454 A114455 this_sequence A114457 A114458 A114459
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 14 2006
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