A386223 Nonsquarefree weak numbers k that are products of primorials.

12, 24, 48, 60, 96, 120, 180, 192, 240, 360, 384, 420, 480, 720, 768, 840, 960, 1080, 1260, 1440, 1536, 1680, 1920, 2160, 2520, 2880, 3072, 3360, 3840, 4320, 4620, 5040, 5760, 6144, 6300, 6480, 6720, 7560, 7680, 8640, 9240, 10080, 11520, 12288, 12600, 12960, 13440

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

Subset of A380543.

Intersection of A025487 and A332785, where A332785 = A052485 \ A005117 = A126706 \ A001694.

The union of this sequence and A364930 is A126706.

Example

Table of n, a(n) and prime decomposition for n = 1..12:
 n   a(n)  prime decomposition
------------------------------
 1    12   2^2 * 3
 2    24   2^3 * 3
 3    48   2^4 * 3
 4    60   2^2 * 3 * 5
 5    96   2^5 * 3
 6   120   2^3 * 3 * 5
 7   180   2^2 * 3^2 * 5
 8   192   2^6 * 3
 9   240   2^4 * 3 * 5
10   360   2^3 * 3^2 * 5
11   384   2^7 * 3
12   420   2^2 * 3 * 5 * 7

Mathematica

(* Load May 19 2018 function f at A025487, then run the following: *)
rad[x_] := Times @@ FactorInteger[x][[All, 1]]; Select[Union@ Flatten[f[6][[3 ;; -1, 2 ;; -1]] ], ! Divisible[#, rad[#]^2] &]

Crossrefs

Cf. A001694, A002110, A007947, A052485, A025487, A055932, A126706, A286708, A332785, A364930, A380543.

Sequence in context: A377590 A102067 A181924 * A367105 A270257 A367361

Adjacent sequences: A386220 A386221 A386222 * A386224 A386225 A386226

Keyword

nonn,easy

Author

Michael De Vlieger, Jul 15 2025

Status

approved