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Search: id:A102445
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| A102445 |
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Number of prime divisors (with multiplicity) of the central trinomial coefficients (A002426). |
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+0
1
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| 0, 1, 1, 1, 2, 2, 2, 4, 2, 2, 3, 2, 2, 4, 3, 4, 6, 3, 2, 3, 3, 5, 6, 6, 4, 9, 3, 3, 2, 3, 3, 4, 5, 3, 5, 4, 2, 3, 3, 4, 2, 7, 5, 7, 7, 5, 5, 6, 6, 4, 5, 8, 9, 4, 5, 6, 3, 3, 7, 6, 8, 7, 7, 4, 5, 4, 4, 7, 7, 9, 11, 5, 8, 7, 7, 6, 7, 7, 8, 12, 4, 7, 6, 6, 4, 8, 7, 4, 10, 7, 7, 6, 6, 7, 5, 5, 6, 8, 7, 9, 10, 5, 7
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Prime central trinomial coefficients by index: 2,3,4,(2000); semiprimes by index: 5,6,7,9,10,12,13,19,29,37,41,108,(125); 3 prime factors by index: 11,15,18,20,21,27,28,30,31,34,38,39,57,58,105,(125)
First occurrence of k: 1,2,5,11,8,22,17,42,52,26,89,71,80,....
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics..
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MATHEMATICA
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bigomega[n_Integer] := Plus @@ Last /@ FactorInteger[n]; tn[n_] := Sum[Binomial[n, k]*Binomial[n - k, k], {k, 0, n/2}]; Table[bigomega[tn[n]], {n, 103}] (from Robert G. Wilson v Feb 21 2005)
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CROSSREFS
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Cf. A002426.
Sequence in context: A102298 A049298 A075016 this_sequence A027389 A160691 A049716
Adjacent sequences: A102442 A102443 A102444 this_sequence A102446 A102447 A102448
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2005
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 21 2005
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