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A127061
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Primes p such that denominator of Sum_{k=1..p-1} 1/k^2 is a square and denominator Sum_{k=1..p-1} 1/k^3 is a cube.
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3
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2, 3, 5, 17, 29, 31, 37, 41, 97, 439, 443, 449, 457, 461, 463, 1009, 1013, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4283, 4289, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511
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OFFSET
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1,1
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LINKS
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FORMULA
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MATHEMATICA
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With[{nn=10000}, Select[Flatten[Position[Denominator[Thread[{Accumulate[1/ Range[ nn]^2], Accumulate[ 1/Range[nn]^3]}]], _?(IntegerQ[Sqrt[First[#]]] && IntegerQ[Surd[Last[#], 3]]&), {1}, Heads->False]], PrimeQ]] (* Harvey P. Dale, Mar 05 2014 *)
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PROG
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(PARI) lista(nn) = {forprime(p = 2, nn, if (issquare(denominator(sum(k=1, p-1, 1/k^2))) && ispower(denominator(sum(k=1, p-1, 1/k^3)), 3), print1(p, ", ")); ); } \\ Michel Marcus, Nov 05 2013
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CROSSREFS
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Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Missing terms in the [9461, 9587] range inserted by Michel Marcus, Nov 05 2013
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STATUS
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approved
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