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A011776
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a(1) = 1; for n > 1, a(n) is defined by the property that n^a(n) divides n! but n^(a(n)+1) does not.
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12
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1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 5, 1, 2, 3, 3, 1, 4, 1, 4, 3, 2, 1, 7, 3, 2, 4, 4, 1, 7, 1, 6, 3, 2, 5, 8, 1, 2, 3, 9, 1, 6, 1, 4, 10, 2, 1, 11, 4, 6, 3, 4, 1, 8, 5, 9, 3, 2, 1, 14, 1, 2, 10, 10, 5, 6, 1, 4, 3, 11, 1, 17, 1, 2, 9, 4, 7, 6, 1, 19, 10, 2, 1, 13, 5, 2, 3, 8, 1, 21
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| The Mathematica code uses Legendre's factorial theorem to quickly compute this sequence. [From T. D. Noe (noe(AT)sspectra.com), Oct 01 2008]
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REFERENCES
| Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery, An Introduction to the Theory Of Numbers, Fifth Edition, John Wiley and Sons, Inc., NY 1991.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 251.
P. Shui, A footnote on the number of times n goes into n!, Math. Gaz., 93 (No. 528, 2009), 492-495. - from N. J. A. Sloane, Jan 21 2010.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Eric W. Weisstein, Math World: Factorial [From T. D. Noe (noe(AT)sspectra.com), Oct 01 2008]
Index entries for sequences related to factorial numbers
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EXAMPLE
| 12^5 divides 12! but 12^6 does not so a(12)=5.
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MAPLE
| a := []; for n from 2 to 200 do i := 0: while n! mod n^i = 0 do i := i+1: od: a := [op(a), i-1]; od: a;
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MATHEMATICA
| Do[m = 1; While[ IntegerQ[ n!/n^m], m++ ]; Print[m - 1], {n, 1, 100} ]
HighestPower[n_, p_] := Module[{r, s=0, k=1}, While[r=Floor[n/p^k]; r>0, s=s+r; k++ ]; s]; SetAttributes[HighestPower, Listable]; Join[{1}, Table[{p, e}=Transpose[FactorInteger[n]]; Min[Floor[HighestPower[n, p]/e]], {n, 2, 100}]] [From T. D. Noe (noe(AT)sspectra.com), Oct 01 2008]
Join[{1}, Table[IntegerExponent[n!, n], {n, 2, 500}]](*From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), 26 Dec 2010*)
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CROSSREFS
| Cf. A011777, A011778, A133481.
Sequence in context: A016727 A054992 A096495 * A098965 A016443 A120256
Adjacent sequences: A011773 A011774 A011775 * A011777 A011778 A011779
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com)
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