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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
OFFSET
1,6
COMMENTS
a(n) > 1 if and only if n is in A049094.
LINKS
Antti Karttunen (terms 1..310) & Hans Havermann, Table of n, a(n) for n = 1..1206
FORMULA
a(n) = A000188(A000225(n)). - R. J. Mathar, Apr 28 2016
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]):
seq(a(n), n=1..105); # Alois P. Heinz, Apr 29 2016
MATHEMATICA
a[n_] := Sqrt[(2^n-1)/Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[2^n -1])];
Array[a, 105] (* Jean-François Alcover, Jan 03 2022 *)
PROG
(PARI) a(n)=core(2^n-1, 1)[2]
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Antti Karttunen, Sep 23 2018
STATUS
approved