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A322797
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Powerful tau numbers.
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1
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1, 8, 9, 36, 72, 108, 128, 225, 288, 441, 625, 864, 972, 1089, 1152, 1521, 1800, 1944, 2000, 2025, 2601, 2700, 3249, 3456, 3528, 3600, 4500, 4761, 5000, 5292, 5625, 6561, 6912, 7569, 7776, 8100, 8649, 8712, 10000, 10800, 12168, 12321, 12348, 13068, 15129, 16000, 16200, 16641, 18000
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OFFSET
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1,2
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COMMENTS
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If the largest exponent among the prime factors of a(n) does not exceed 2 then A046692(a(n)) = sqrt(a(n)), otherwise A046692(a(n)) = 0.
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LINKS
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EXAMPLE
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MATHEMATICA
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powtauQ[1] = True; powtauQ[n_] := Min[e = (Last /@ FactorInteger[n])] > 1 && Divisible[n, Times @@ (e + 1)]; Select[Range[18000], powtauQ] (* Amiram Eldar, Dec 30 2019 *)
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PROG
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(PARI) isok(n) = ispowerful(n) && ((n % numdiv(n)) == 0); \\ Michel Marcus, Jan 16 2019
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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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