

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
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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



