

A205562


Least positive integer j such that n divides (2k)!(2j)!, where k, as in A205561, is the least number for which there is such a j.


0



1, 1, 2, 2, 3, 2, 4, 2, 3, 3, 1, 2, 7, 4, 3, 3, 9, 3, 1, 3, 4, 1, 2, 2, 3, 7, 5, 4, 2, 3, 1, 4, 3, 9, 4, 3, 19, 1, 7, 3, 4, 4, 1, 3, 3, 2, 2, 3, 4, 3, 9, 7, 1, 5, 3, 4, 5, 2, 12, 3, 4, 1, 4, 4, 7, 3, 1, 9, 2, 4, 2, 3, 2, 19, 3, 5, 6, 7, 2, 3, 5, 4, 12, 4, 9, 1, 2, 3, 4, 3, 7, 2, 6, 2, 5, 4, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

For a guide to related sequences, see A204892.


LINKS



EXAMPLE

1 divides (2*2)!(2*1)! > k=2, j=1
2 divides (2*2)!(2*1)! > k=2, j=1
3 divides (2*3)!(2*2)! > k=3, j=2
4 divides (2*3)!(2*2)! > k=3, j=2
5 divides (2*4)!(2*3)! > k=4, j=3


MATHEMATICA

s = Table[(2n)!, {n, 1, 120}];
lk = Table[NestWhile[# + 1 &, 1,
Min[Table[Mod[s[[#]]  s[[j]], z], {j, 1, #  1}]] =!= 0 &], {z, 1, Length[s]}]
Table[NestWhile[# + 1 &, 1,
Mod[s[[lk[[j]]]]  s[[#]], j] =!= 0 &], {j, 1, Length[lk]}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



