

A122417


Factorials from an irrationality measure for e, with a(1) = 2.


4



2, 6, 24, 120, 720, 24, 40320, 120, 5040, 720, 479001600, 120, 87178291200, 40320, 720, 5040, 6402373705728000, 5040, 2432902008176640000, 720, 40320, 479001600, 620448401733239439360000, 120, 39916800, 87178291200, 3628800, 40320
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OFFSET

1,1


COMMENTS

If n > 1, then a(n) is the smallest factorial such that e  m/n > 1/a(n) for any integer m.
a(n) is the second smallest factorial divisible by n.


LINKS

Table of n, a(n) for n=1..28.
Mohammad K. Azarian, Euler's Number Via Difference Equations, International Journal of Contemporary Mathematical Sciences, Vol. 7, 2012, No. 22, pp. 1095  1102.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637641.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 20072010.
Index entries for sequences related to factorial numbers.


FORMULA

a(n) = (A002034(n)+1)! = A122416(n)!.


EXAMPLE

a(6) = (S(6)+1)! = (3+1)! = 24.


MATHEMATICA

nmax = 28;
Do[m = 1; While[!IntegerQ[m!/n], m++]; a[n] = (m+1)!, {n, 1, nmax}];
Array[a, nmax] (* JeanFrançois Alcover, Dec 04 2018 *)


CROSSREFS

Cf. A001113, A002034, A092495, A122416.
Sequence in context: A297204 A071088 A177533 * A321008 A033644 A212309
Adjacent sequences: A122414 A122415 A122416 * A122418 A122419 A122420


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Sep 03 2006


STATUS

approved



