A330873 Numbers with a record number of divisors that are perfect powers (A091050).

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

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..86

Amiram Eldar, Table of n, a(n), A091050(a(n)) for n = 1..86

Example

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.

Mathematica

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

Crossrefs

Subsequence of A025487.

Cf. A001597, A091050.

Sequence in context: A085629 A349111 A307870 * A233442 A373969 A046055

Adjacent sequences: A330870 A330871 A330872 * A330874 A330875 A330876

Keyword

nonn

Author

Amiram Eldar, Apr 29 2020

Status

approved