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

Author

Alex Ratushnyak, Aug 11 2012

Keywords

• nonn

Comments

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

Examples

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

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!).

Programs

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 *)

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