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Search: id:A114504
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| A114504 |
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Numbers n such that the n-th hexagonal number is a 6-almost prime. |
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+0
1
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| 50, 56, 60, 63, 81, 95, 98, 112, 116, 120, 138, 150, 152, 158, 172, 180, 182, 189, 196, 199
(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 A046306. n such that A001222(A000384(n)) = 6. n such that A001222(n*(2*n-1)) = 6.
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EXAMPLE
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a(1) = 50 because HexagonalNumber(50) = H(50) = 50*(2*50-1) = 4950 = 2 * 3^2 * 5^2 * 11 is a 6-almost prime.
a(2) = 56 because H(56) = 56*(2*56-1) = 6216 = 2^3 * 3 * 7 * 37 is a 6-almost prime.
a(5) = 81 because H(81) = 81*(2*81-1) = 13041 = 3^4 * 7 * 23 is a 6-almost prime.
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CROSSREFS
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Cf. A000384, A001222, A046306.
Sequence in context: A081646 A052261 A118146 this_sequence A046832 A046834 A046836
Adjacent sequences: A114501 A114502 A114503 this_sequence A114505 A114506 A114507
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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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