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A127045
Primes p such that denominator of Sum_{k=1..p-1} 1/k^9 is a 9th power.
1
2, 3, 5, 11, 13, 17, 29, 31, 37, 97, 127, 131, 251, 257, 263, 293, 431, 433, 439, 443, 449, 457, 461, 463, 467, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3797, 3803, 3821, 3823, 3833, 3907, 3911, 3917
OFFSET
1,1
MATHEMATICA
d[n_] := Module[{}, su = 0; a = {}; For[i = 1, i <= n, i++, su = su + 1/ i^9; If[PrimeQ[i + 1], If[IntegerQ[(Denominator[su])^(1/9)], AppendTo[a, i + 1]]]]; a] d[2000]
Select[Flatten[Position[Denominator[Accumulate[1/Range[4000]^9]], _?(IntegerQ[ Surd[ #, 9]]&)]]+1, PrimeQ] (* Harvey P. Dale, Aug 06 2022 *)
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 04 2007
STATUS
approved