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A346465
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Numbers k such that (4^k - 2)*(4^k - 1)/Clausen(2*k, 1) is not squarefree, where Clausen(n, m) = A160014(n, m).
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1
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9, 11, 18, 27, 32, 36, 45, 50, 53, 54, 63, 68, 72, 74, 78, 81, 90, 95, 99, 100, 108, 116, 117, 126, 127, 135, 137, 144, 147, 150, 153, 155, 158, 162, 171, 179, 180, 182, 189, 198, 200, 204, 207, 216, 221, 225, 233, 234, 242, 243, 250, 252, 261, 263, 270, 279
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OFFSET
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1,1
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COMMENTS
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Also numbers k such that 6*GaussBinomial(2*k, 2, 2)/denominator(Bernoulli(2*k, 1)) is not squarefree.
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LINKS
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FORMULA
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The positive multiples of 9 form a subsequence.
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MAPLE
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with(NumberTheory): isa := n -> not IsSquareFree(((4^n - 2)*(4^n - 1))/
mul(i, i = select(isprime, map(i -> i+1, Divisors(2*n))))):
select(isa, [$(1..100)]);
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MATHEMATICA
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q[n_] := Product[k, {k, Select[Table[d + 1, {d, Divisors[2 n]}], PrimeQ]}];
isA[n_] := ! SquareFreeQ[((4^n - 2) (4^n -1)) / q[n]];
Select[Range[50], isA]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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