A379554 - OEIS

%I #6 Dec 30 2024 17:09:57

%S 1,2,3,4,6,8,9,10,12,14,18,20,21,24,26,27,28,30,32,36,40,42,48,52,54,

%T 56,60,64,72,78,80,90,96,100,108,114,120,126,128,135,136,144,150,160,

%U 168,170,176,180,186,192,200,204,210,224,240,248,252,264,272,280,288

%N Records in A379552.

%H Michael De Vlieger, <a href="/A379554/b379554.txt">Table of n, a(n) for n = 1..212</a>

%t r = 0; nn = 10^9;

%t rad[x_] := Times @@ FactorInteger[x][[All, 1]];

%t s = Union@ Select[Flatten@ Table[a^2*b^3, {b, Surd[nn, 3]}, {a, Sqrt[nn/b^3]}],

%t   Length@ Select[FactorInteger[#][[All, -1]], # > 2 &] >= 2 &]; nn = Length[s];

%t Reap[Do[k = s[[i]]; If[# > r, r = #; Sow[r]] &@

%t   Count[Transpose@ {#, k/#} &@ #[[2 ;; Ceiling[Length[#]/2]]] &@ Divisors[k],

%t     _?(And[1 < GCD @@ {##},

%t     rad[#1] == rad[#2],

%t     Mod[#1, #2] != 0,

%t     Mod[#2, #1] != 0] & @@ # &)], {i, nn}] ][[-1, 1]]

%Y Cf. A376936, A379552, A379553.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Dec 25 2024