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Search: id:A100934
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| A100934 |
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Numbers having more than one representation as the product of consecutive integers. |
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+0
1
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| 6, 24, 120, 210, 720, 5040, 40320, 175560, 362880, 3628800, 17297280, 19958400, 39916800, 259459200, 479001600, 6227020800, 87178291200
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All the factorials occur because we allow products to start with 1. See A064224 for a more restrictive case.
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REFERENCES
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H. L. Abbott, P. Erdos and D Hanson, On the number of times an integer occurs as a binomial coefficient, Amer. Math. Monthly, Vol. 81, No. 3 (Mar., 1974), 256-261.
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EXAMPLE
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120 is here because 120 = 2*3*4*5 = 4*5*6.
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MATHEMATICA
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nn=10^10; t3={}; Do[m=0; p=n; While[m++; p=p(n+m); p<=nn, t3={t3, p}], {n, Sqrt[nn]}]; t3=Sort[Flatten[t3]]; lst={}; Do[If[t3[[i]]==t3[[i+1]], AppendTo[lst, t3[[i]]]], {i, Length[t3]-1}]; Union[lst]
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CROSSREFS
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Cf. A064224, A003015 (numbers occurring 5 or more times in Pascal's triangle).
Sequence in context: A038380 A052745 A109583 this_sequence A127917 A026982 A051197
Adjacent sequences: A100931 A100932 A100933 this_sequence A100935 A100936 A100937
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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), Nov 22 2004
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