This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380446 #67 Aug 02 2025 15:53:01
%S A380446 36,144,216,324,576,900,1296,1728,2304,2916,3600,5184,5832,7776,8100,
%T A380446 9216,11664,13824,14400,20736,22500,26244,27000,32400,36864,44100,
%U A380446 46656,57600,72900,82944,90000,104976,110592,129600,147456,157464,176400,186624,202500,216000
%N A380446 Perfect powers k^m, m > 1, omega(k) > 1, such that A053669(k) > A006530(k), where omega = A001221.
%C A380446 Perfect powers k^m, m > 1, for k in A055932.
%C A380446 Union of {k^m : rad(k) | P(i), m >= 2}, rad = A007947, P = A002110. Therefore perfect powers in A033845, A143207, A147571, A147572, etc. are proper subsets.
%C A380446 Terms are even. For a(n) such that omega(a(n)) > 2, a(n) mod 10 = 0, where omega = A001221.
%H A380446 Michael De Vlieger, <a href="/A380446/b380446.txt">Table of n, a(n) for n = 1..16384</a>
%H A380446 Michael De Vlieger, <a href="/A380446/a380446.txt">Fast Mathematica algorithm for A055932</a>.
%F A380446 Intersection of A131605 and A055932 = A304250 \ A246547.
%e A380446 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. Terms that also appear in A368682 are marked by "#":
%e A380446 Exponents
%e A380446 n a(n) 2.3.5.7.11
%e A380446 -----------------------------------
%e A380446 1 36 = 6^2 # 2.2
%e A380446 2 144 = 12^2 # 4.2
%e A380446 3 216 = 6^3 # 3.3
%e A380446 4 324 = 18^2 2.4
%e A380446 5 576 = 24^2 # 6.2
%e A380446 6 900 = 30^2 # 2.2.2
%e A380446 7 1296 = 6^4 # 4.4
%e A380446 8 1728 = 12^3 # 6.3
%e A380446 9 2304 = 48^2 # 8.2
%e A380446 10 2916 = 54^2 2.6
%e A380446 11 3600 = 60^2 # 4.2.2
%e A380446 12 5184 = 72^2 # 6.4
%e A380446 26 44100 = 210^2 # 2.2.2.2
%e A380446 90 5336100 = 2310^2 # 2.2.2.2.2
%t A380446 (* Load linked Mathematica algorithm, then: *)
%t A380446 Select[Union@ Flatten[a055932[7][[3 ;; -1, 2 ;; -1]] ], And[Divisible[#1, Apply[Times, #2[[All, 1]] ]^2], GCD @@ #2[[All, -1]] > 1] & @@ {#, FactorInteger[#]} &]
%Y A380446 Cf. A001597, A002110, A006530, A007947, A033845, A053669, A055932, A126706, A131605, A143207, A147571, A147572, A246547, A304250, A365308 (subset), A368682 (subset), A369374 (superset).
%K A380446 nonn
%O A380446 1,1
%A A380446 _Michael De Vlieger_, Jul 25 2025