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A215454 a(n) = least positive k such that n^2 divides k! 0
1, 4, 6, 6, 10, 6, 14, 8, 9, 10, 22, 6, 26, 14, 10, 10, 34, 9, 38, 10, 14, 22, 46, 8, 20, 26, 15, 14, 58, 10, 62, 12, 22, 34, 14, 9, 74, 38, 26, 10, 82, 14, 86, 22, 10, 46, 94, 10, 28, 20, 34, 26, 106, 15, 22, 14, 38, 58, 118, 10, 122, 62, 14, 16, 26, 22, 134, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Indices n such that a(n)=n: 1 followed by A074845.

LINKS

Table of n, a(n) for n=1..68.

EXAMPLE

a(12): least positive k such that 144 divides k! is k=6, 6!=720. So a(12)=6.

MATHEMATICA

Module[{nn=200, f}, f=Range[nn]!; Position[f, #]&/@Table[SelectFirst[ f, Divisible[ #, n^2]&], {n, nn}]]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 11 2018 *)

PROG

(Python)

TOP = 77

ii = [0]*TOP

for i in range(1, TOP):

    ii[i] = i*i

f = k = y = 1

res = [-1]*TOP

while y<TOP:

    for i in range(1, TOP):

      if res[i]<0 and f % ii[i] == 0:

        res[i] = k

        y += 1

    k += 1

    f *= k

for i in range(1, TOP):

    print res[i],

CROSSREFS

Cf. A002034 (least k such that n divides k!).

Cf. A085779 (least k such that triangular(n) divides k!).

Cf. A093896 (least positive k such that n^n divides k!).

Sequence in context: A323674 A183986 A160995 * A155750 A159475 A098350

Adjacent sequences:  A215451 A215452 A215453 * A215455 A215456 A215457

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Aug 11 2012

STATUS

approved

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Last modified August 17 11:14 EDT 2019. Contains 326057 sequences. (Running on oeis4.)