A330873 - OEIS

%I #14 Apr 30 2020 03:25:25

%S 1,4,8,16,32,64,128,256,432,576,1152,1296,1728,3456,5184,10368,15552,

%T 20736,41472,46656,82944,129600,259200,331776,373248,518400,746496,

%U 1036800,1166400,2073600,3240000,4665600,6350400,12700800,12960000,18662400,25401600,50803200

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

%H Amiram Eldar, <a href="/A330873/b330873.txt">Table of n, a(n) for n = 1..86</a>

%H Amiram Eldar, <a href="/A330873/a330873.txt">Table of n, a(n), A091050(a(n)) for n = 1..86</a>

%e 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.

%t 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

%Y Subsequence of A025487.

%Y Cf. A001597, A091050.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 29 2020