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Search: id:A073840
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| A073840 |
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Product of the composite numbers between n and 2n (both inclusive). |
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+0
3
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| 1, 4, 24, 192, 4320, 51840, 120960, 29030400, 65318400, 145152000, 6706022400, 160944537600, 8717829120000, 6590678814720000, 14122883174400000, 30128817438720000, 2112783322890240000, 2662106986841702400000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) is divisible by central binomial coefficients, A001405[n]
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FORMULA
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a(n)=A049614(2n)/A049614(n-1)
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EXAMPLE
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a(6) = 6*8*9*10*12 = 51840.
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MAPLE
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for n from 1 to 50 do l := 1:for j from n to 2*n do if not isprime(j) then l := l*j:fi:od:a[n] := l:od:seq(a[j], j=1..50);
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MATHEMATICA
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cs[x_] := Flatten[Position[Table[PrimeQ[j], {j, x, 2*x}], False]]+x-1; prcs[x_] := Apply[Times, cs[x]]; Table[prcs[w], {w, 1, 25}]
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PROGRAM
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(PARI) a(n)=prod(i=n, 2*n, i^if(isprime(i), 0, 1))
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CROSSREFS
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Cf. A073839, A073641.
Sequence in context: A088815 A036691 A002866 this_sequence A024249 A007145 A101370
Adjacent sequences: A073837 A073838 A073839 this_sequence A073841 A073842 A073843
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 13 2002
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EXTENSIONS
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More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de) and Labos E. (labos(AT)ana.sote.hu), Aug 14 2002
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