

A330873


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


1



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

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: A005934 A085629 A307870 * A233442 A046055 A186949
Adjacent sequences: A330870 A330871 A330872 * A330874 A330875 A330876


KEYWORD

nonn


AUTHOR

Amiram Eldar, Apr 29 2020


STATUS

approved



