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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

%I

%S 1,6,15,18,12,32,24,36,40,45,48,100,84,60,154,165,72,96,80,126,90,135,

%T 286,200,312,264,168,120,297,189,160,330,544,210,144,224,300,385,396,

%U 324,252,680,350,180,280,748,572,486,400,405,315,528,320,336,450,512,288,240,715

%N 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!.

%C Least k such that A011776(k)=n.

%C 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

%C First 10000 terms are 163-smooth. - _David A. Corneth_, Mar 15 2019

%D 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.

%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 251.

%H David A. Corneth, <a href="/A133481/b133481.txt">Table of n, a(n) for n = 1..10000</a> (first 1150 terms form T. D. Noe and Robert G. Wilson v)

%H David A. Corneth, <a href="/A133481/a133481_2.gp.txt">PARI program</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%e a(7)=24 because 24^7|24! and smaller numbers than 24 do not divide their factorials 7 times.

%e 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

%t 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 *)

%o (PARI) a(n)=if(n<2,1,my(k=2);while(valuation(k!,k)!=n,k++);k) \\ _Charles R Greathouse IV_, Feb 27 2012

%o (PARI) See Corneth link \\ _David A. Corneth_, Mar 15 2019

%Y Cf. A011776, A011777, A011778.

%K nonn,look,nice

%O 1,2

%A _Masahiko Shin_, Nov 29 2007

%E Edited by _N. J. A. Sloane_ using material from A011777, Nov 29 2007

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Last modified June 24 13:17 EDT 2019. Contains 324325 sequences. (Running on oeis4.)