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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!. 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

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 (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 24^7|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

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

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Last modified May 21 21:28 EDT 2019. Contains 323444 sequences. (Running on oeis4.)