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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 (list; graph; refs; listen; history; text; internal format)
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 163-smooth. - 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 (terms 1..345 from T. D. Noe, terms 346..1150 from Robert G. Wilson v)
David A. Corneth, PARI program.
EXAMPLE
a(7)=24 because 24^7|24! and smaller numbers than 24 do not divide their factorials 7 times.
a(2) = 6 as 6^2|6! 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
Sequence in context: A351472 A139204 A122661 * A274549 A351175 A099535
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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)