|
|
A272334
|
|
Square root of the largest square dividing 2^n - 1.
|
|
1
|
|
|
1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 5, 7, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 21, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 15, 1, 1, 7, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 1, 21, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 1, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
a(n) > 1 if and only if n is in A049094.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
2^42 - 1 = 3^2 * 7^2 * 43 * 127 * 337 * 5419, so a(42) = 3*7 = 21.
|
|
MAPLE
|
a:= n-> mul(i[1]^iquo(i[2], 2), i=ifactors(2^n-1)[2]):
|
|
MATHEMATICA
|
a[n_] := Sqrt[(2^n-1)/Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[2^n -1])];
|
|
PROG
|
(PARI) a(n)=core(2^n-1, 1)[2]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|