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Search: id:A110496
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| A110496 |
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Least k such that prime(n)^3 divides binomial(2k,k). |
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+0
2
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| 7, 14, 63, 172, 666, 1099, 2457, 3430, 6084, 12195, 14896, 25327, 34461, 39754, 51912, 74439, 102690, 113491, 150382, 178956, 194509, 246520, 285894, 352485, 456337, 515151, 546364, 612522, 647515, 721449, 1024192, 1124046, 1285677
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For prime p > (2n)^(1/3), p^3 does not divide binomial(2n,n).
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FORMULA
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a(n)=(prime(n)^3+1)/2 for n>1
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MATHEMATICA
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t3=Table[f=FactorInteger[Binomial[2n, n]]; s=Select[f, #[[2]]>2&]; If[s=={}, 0, s[[ -1, 1]]], {n, 15000}]; Table[p=Prime[i]; First[Flatten[Position[t3, p]]], {i, PrimePi[Max[t3]]}]
lst={7}; Do[AppendTo[lst, (DivisorSigma[3, Prime[n]])/2], {n, 2, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
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CROSSREFS
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Cf. A110495 (n such that binomial(2n, n) is cubefree).
Sequence in context: A033650 A135536 A020700 this_sequence A117867 A143682 A080451
Adjacent sequences: A110493 A110494 A110495 this_sequence A110497 A110498 A110499
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 22 2005
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