

A133481


a(1) = 1, for n > 1, a(n) is the least k such that k^n divides k! but k^(n+1) does not divide k!.


6



1, 6, 15, 18, 12, 32, 24, 36, 40, 45, 48, 100, 84, 60, 154, 165, 72, 96, 80, 126, 90, 135, 286, 200, 312, 264, 168, 120, 297, 189, 160, 330, 544, 210, 144, 224, 300, 385, 396, 324, 252, 680, 350, 180, 280, 748, 572, 486, 400, 405, 315, 528, 320, 336, 450, 512, 288, 240, 715
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OFFSET

1,2


COMMENTS

Least k such that A011776(k)=n.
New record highs, by index: 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 15, 16, 23, 25, 32, 33, 42, 46, 63, 66, 79, 85, 100, 119, 128, 167, 188, 201, 213, 226, 240, 256, 335, 346, 348, 352, 360, 377, 385, 414, 426, 480, 481, 494, 504, 533, 555, 596, 656, 727, 883, 926, 938, 1026, 1094, ...  Robert G. Wilson v, Feb 28 2012
First 10000 terms are 163smooth.  David A. Corneth, Mar 15 2019


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.


LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1150 terms form T. D. Noe and Robert G. Wilson v)
David A. Corneth, PARI program
Index entries for sequences related to factorial numbers


EXAMPLE

a(7)=24 because 24^724! and smaller numbers than 24 do not divide their factorials 7 times.
a(2) = 6 as 6^26! but 6! doesn't divide 6^(2 + 1) and 6 is the least positive integer with this property.  David A. Corneth, Mar 15 2019


MATHEMATICA

kdn[n_]:=Module[{k=2}, While[!Divisible[k!, k^n]Divisible[k!, k^(n+1)], k++]; k]; Join[{1}, Array[kdn, 60, 2]] (* Harvey P. Dale, Feb 27 2012 *)


PROG

(PARI) a(n)=if(n<2, 1, my(k=2); while(valuation(k!, k)!=n, k++); k) \\ Charles R Greathouse IV, Feb 27 2012
(PARI) See Corneth link \\ David A. Corneth, Mar 15 2019


CROSSREFS

Cf. A011776, A011777, A011778.
Sequence in context: A158338 A139204 A122661 * A274549 A099535 A302296
Adjacent sequences: A133478 A133479 A133480 * A133482 A133483 A133484


KEYWORD

nonn,look,nice


AUTHOR

Masahiko Shin, Nov 29 2007


EXTENSIONS

Edited by N. J. A. Sloane using material from A011777, Nov 29 2007


STATUS

approved



