A380452 Perfect powers k^m, m > 1, omega(k) > 1, such that A053669(k) > A006530(k) that are not also products of primorials, where omega = A001221.

324, 2916, 5832, 8100, 11664, 22500, 26244, 72900, 90000, 104976, 157464, 202500, 236196, 291600, 360000, 396900, 419904, 562500, 656100, 729000, 944784, 1102500, 1259712, 1440000, 1822500, 1889568, 2125764, 2160900, 2250000, 2624400, 3375000, 3572100, 3779136

Offset: 1

Author

Michael De Vlieger, Jul 25 2025

Keywords

• nonn

Comments

Perfect powers k^m, m > 1, for composite k in A056808.

Terms are even. For a(n) such that omega(a(n)) > 2, a(n) mod 10 = 0, where omega = A001221.

Examples

			Table of n, a(n) for select n, showing exponents m of prime power factors p^m | a(n) for primes p listed in the heading:
                      Exponents
 n      a(n)          2.3.5
-------------------------------
 1      324 =  18^2   2.4
 2     2916 =  54^2   2.6
 3     5832 =  18^3   3.6
 4     8100 =  90^2   2.4.2
 5    11664 = 108^2   4.6
 6    22500 = 150^2   2.2.4
 7    26244 = 162^2   2.8
 8    72900 = 270^2   2.6.2
 9    90000 = 300^2   4.2.4
10   104976 =  18^4   4.8
11   157464 =  54^3   3.9
12   202500 = 450^2   2.4.4
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..16384
• Michael De Vlieger, Fast Mathematica algorithm for A055932.

Crossrefs

Cf. A001597, A002110, A006530, A007947, A053669, A055932, A131605, A246547, A304250, A368682, A369374, A380446.

Programs

Mathematica

(* Load linked Mathematica algorithm, then: *)
Select[Union@ Flatten[a055932[7][[3 ;; -1, 2 ;; -1]] ], And[Divisible[#1, Apply[Times, #2[[All, 1]] ]^2], GCD @@ #2[[All, -1]] > 1] & @@ {#, FactorInteger[#]} &]

Formula

Intersection of A131605 and A056808 = A380446 \ A368682.

Set difference A380446 \ A025487.