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A330873
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Numbers with a record number of divisors that are perfect powers (A091050).
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1
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1, 4, 8, 16, 32, 64, 128, 256, 432, 576, 1152, 1296, 1728, 3456, 5184, 10368, 15552, 20736, 41472, 46656, 82944, 129600, 259200, 331776, 373248, 518400, 746496, 1036800, 1166400, 2073600, 3240000, 4665600, 6350400, 12700800, 12960000, 18662400, 25401600, 50803200
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1 has one divisor that is a perfect power, 1. The next number with more than one perfect power divisor is 4, with 2 such divisors, 1 and 4. Therefore a(2) = 4.
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MATHEMATICA
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powDivNum[n_] := 1 + DivisorSum[n, 1 &, GCD @@ FactorInteger[#][[;; , 2]] > 1 &]; dm = 0; seq = {}; Do[d = powDivNum[n]; If[d > dm, dm = d; AppendTo[seq, n]], {n, 1, 10^6}]; seq
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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