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A124781
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GCD(d(n), d(n+2)) where d(n) = GCD(n!, A(n)) and A(n) = A000522(n) = Sum_{k=0..n} n!/k!).
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3
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1, 1, 1, 2, 1, 2, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 2, 1, 2, 5, 26, 1, 2, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 13, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 26, 1, 2, 5, 2, 1, 2, 1, 10, 1, 2, 1, 2, 65, 2, 1, 2, 1, 10, 1, 2, 1, 74, 5, 2, 1, 26, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 13, 2, 1, 2, 5, 2, 1, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) divides n+3 because A(n+2) = (n+2)(n+1)*A(n) + n+3.
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REFERENCES
| J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
| Index entries for sequences related to factorial numbers
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
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FORMULA
| a(n) = GCD(A093101(n), A093101(n+2)) = (n+3)/A123901(n)
a(n) = GCD(A(n), A(n+2), n!) where A(n)=1+n+n(n-1)+...+n! - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Nov 13 2006
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EXAMPLE
| a(3) = GCD(d(3),d(5)) = GCD(GCD(3!,16), GCD(5!,326)) = GCD(2,2) =
2
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MATHEMATICA
| (A[n_] := Sum[n!/k!, {k, 0, n}]; d[n_] := GCD[n!, A[n]]; Table[GCD[d[n], d[n+2]], {n, 0, 100}])
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CROSSREFS
| Cf. A000522, A093101, A123899, A123900, A123901, A124779, A124780, A124782.
Sequence in context: A066772 A104060 A062347 * A124151 A110179 A071559
Adjacent sequences: A124778 A124779 A124780 * A124782 A124783 A124784
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KEYWORD
| nonn
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AUTHOR
| Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Nov 07 2006
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