A215454 a(n) = least positive k such that n^2 divides k!

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

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