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 A133481 Least k such that k^n divides k! but k^(n+1) does not divide k!. 5
 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 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 T. D. Noe and Robert G. Wilson v, Table of n, a(n) for n = 1..1150 (T. D. Noe produced 345 terms) EXAMPLE a(7)=24 because 24^7|24! and smaller numbers than 24 do not divide their factorials 7 times. 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 CROSSREFS Cf. A011776, A011777, A011778. Sequence in context: A158338 A139204 A122661 * A274549 A099535 A302296 Adjacent sequences:  A133478 A133479 A133480 * A133482 A133483 A133484 KEYWORD nice,nonn 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 December 17 00:41 EST 2018. Contains 318191 sequences. (Running on oeis4.)