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 A368681 #7 Jan 03 2024 03:37:03
%S A368681 1,4,8,16,32,36,64,128,144,216,256,512,576,900,1024,1296,1728,2048,
%T A368681 2304,3600,4096,5184,7776,8192,9216,13824,14400,16384,20736,27000,
%U A368681 32400,32768,36864,44100,46656,57600,65536,82944,110592,129600,131072,147456,176400,186624
%N A368681 Products of primorials that are perfect powers.
%C A368681 Intersection of A025487 and A001597.
%C A368681 Contains A365308 (perfect powers of composite primorials), A368508 (perfect powers of composite superprimorials), and A368682.
%C A368681 These numbers are perfect powers of some smaller product of primorials.
%H A368681 Michael De Vlieger, <a href="/A368681/b368681.txt">Table of n, a(n) for n = 1..10000</a>
%e A368681 Let b(n) = A025487(n).
%e A368681 a(1) = b(1) = 1 = 1^k = b(1)^k, k >= 2,
%e A368681 a(2) = b(3) = 4 = 2^2 = b(2)^2,
%e A368681 a(3) = b(5) = 8 = 2^3 = b(2)^3,
%e A368681 a(6) = b(11) = 36 = 6^2 = b(4)^2,
%e A368681 a(9) = b(19) = 144 = 12^2 = b(6)^2, etc.
%e A368681 2 is not in the sequence since 2 is squarefree and not in A001597.
%t A368681 {1}~Join~Select[Range[4, 200000, 2], Or[PrimePowerQ[#], And[Union@ Differences@ PrimePi@ #1 == {1}, AllTrue[Union@ Differences@ #2, # <= 0 &], GCD @@ #2 > 1] & @@ Transpose@ FactorInteger[#]] &]
%Y A368681 Cf. A000079, A001597, A002110, A025487, A131605, A365308, A368508, A368682.
%K A368681 nonn
%O A368681 1,2
%A A368681 _Michael De Vlieger_, Jan 02 2024