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Search: id:A114441
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| A114441 |
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Indices of 3-almost prime pentagonal numbers. |
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1
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| 3, 7, 8, 9, 17, 18, 20, 21, 22, 23, 25, 26, 28, 30, 31, 37, 44, 49, 50, 61, 62, 65, 66, 69, 71, 74, 76, 78, 79, 85, 89, 93, 97, 98, 113, 116, 121, 122, 125, 129, 130, 133, 137, 141, 145, 148, 151, 154, 157, 158, 161, 164, 166, 170, 173, 174, 178
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k-1) or k*((3*k-1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k-1)/2 prime] or [k/2 prime and 3*k-1 prime].
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LINKS
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Eric Weisstein's World of Mathematics, Pentagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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{a(n)} = {k such that A001222(A000326(k)) = 3}. {a(n)} = {k such that k*(3*k-1)/2 has exactly 3 prime factors}. {a(n)} = {k such that A000326(k) is an element of A014612}.
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EXAMPLE
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a(1) = 3 because P(3) = PentagonalNumber(3) = 3*(3*3 -1)/2 = 12 = 2^2 * 3 is a 3-almost prime.
a(2) = 7 because P(7) = 7*(3*7 -1)/2 = 70 = 2 * 5 * 7 is a 3-almost prime.
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CROSSREFS
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Cf. A000326, A001222, A014612, A115709.
Adjacent sequences: A114438 A114439 A114440 this_sequence A114442 A114443 A114444
Sequence in context: A112680 A096079 A094551 this_sequence A043046 A030674 A030684
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 14 2006
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