login
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
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
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