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A386223 Nonsquarefree weak numbers k that are products of primorials.

%I A386223 #11 Jul 21 2025 13:14:28
%S A386223 12,24,48,60,96,120,180,192,240,360,384,420,480,720,768,840,960,1080,
%T A386223 1260,1440,1536,1680,1920,2160,2520,2880,3072,3360,3840,4320,4620,
%U A386223 5040,5760,6144,6300,6480,6720,7560,7680,8640,9240,10080,11520,12288,12600,12960,13440
%N A386223 Nonsquarefree weak numbers k that are products of primorials.
%H A386223 Michael De Vlieger, <a href="/A386223/b386223.txt">Table of n, a(n) for n = 1..10000</a>
%F A386223 Subset of A380543.
%F A386223 Intersection of A025487 and A332785, where A332785 = A052485 \ A005117 = A126706 \ A001694.
%F A386223 The union of this sequence and A364930 is A126706.
%e A386223 Table of n, a(n) and prime decomposition for n = 1..12:
%e A386223  n   a(n)  prime decomposition
%e A386223 ------------------------------
%e A386223  1    12   2^2 * 3
%e A386223  2    24   2^3 * 3
%e A386223  3    48   2^4 * 3
%e A386223  4    60   2^2 * 3 * 5
%e A386223  5    96   2^5 * 3
%e A386223  6   120   2^3 * 3 * 5
%e A386223  7   180   2^2 * 3^2 * 5
%e A386223  8   192   2^6 * 3
%e A386223  9   240   2^4 * 3 * 5
%e A386223 10   360   2^3 * 3^2 * 5
%e A386223 11   384   2^7 * 3
%e A386223 12   420   2^2 * 3 * 5 * 7
%t A386223 (* Load May 19 2018 function f at A025487, then run the following: *)
%t A386223 rad[x_] := Times @@ FactorInteger[x][[All, 1]]; Select[Union@ Flatten[f[6][[3 ;; -1, 2 ;; -1]] ], ! Divisible[#, rad[#]^2] &]
%Y A386223 Cf. A001694, A002110, A007947, A052485, A025487, A055932, A126706, A286708, A332785, A364930, A380543.
%K A386223 nonn,easy
%O A386223 1,1
%A A386223 _Michael De Vlieger_, Jul 15 2025