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A100934 Numbers having more than one representation as the product of consecutive integers. 0
6, 24, 120, 210, 720, 5040, 40320, 175560, 362880, 3628800, 17297280, 19958400, 39916800, 259459200, 479001600, 6227020800, 87178291200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All the factorials occur because we allow products to start with 1. See A064224 for a more restrictive case.

LINKS

Table of n, a(n) for n=1..17.

H. L. Abbott, P. Erdos and D. Hanson, On the numbers of times an integer occurs as a binomial coefficient, Amer. Math. Monthly, (March 1974), 256-261.

EXAMPLE

120 is here because 120 = 2*3*4*5 = 4*5*6.

MATHEMATICA

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]

CROSSREFS

Cf. A064224, A003015 (numbers occurring 5 or more times in Pascal's triangle).

Sequence in context: A293236 A217193 A109583 * A127917 A293118 A293121

Adjacent sequences:  A100931 A100932 A100933 * A100935 A100936 A100937

KEYWORD

nonn,more

AUTHOR

T. D. Noe, Nov 22 2004

STATUS

approved

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Last modified February 22 16:26 EST 2019. Contains 320399 sequences. (Running on oeis4.)