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 A322793 #15 Mar 10 2024 04:02:08
%S A322793 4,8,16,32,36,64,128,216,256,512,900,1024,1296,2048,4096,7776,8192,
%T A322793 16384,27000,32768,44100,46656,65536,131072,262144,279936,524288,
%U A322793 810000,1048576,1679616,2097152,4194304,5336100,8388608,9261000
%N A322793 Proper powers of primorial numbers.
%C A322793 A primorial number is a product of the first n primes, for some n.
%C A322793 Also Heinz numbers of non-strict uniform integer partitions whose union is an initial interval of positive integers. An integer partition is uniform if all parts appear with the same multiplicity. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A322793 Michael De Vlieger, <a href="/A322793/b322793.txt">Table of n, a(n) for n = 1..8255</a>
%F A322793 Sum_{n>=1} 1/a(n) = Sum_{k>=1} 1/(A002110(k)*(A002110(k)-1)) = 0.53450573145072369022... . - _Amiram Eldar_, Mar 10 2024
%e A322793 The sequence of all non-strict uniform integer partitions whose Heinz numbers belong to the sequence begins: (11), (111), (1111), (11111), (2211), (111111), (1111111), (222111), (11111111), (111111111), (332211), (1111111111), (22221111).
%t A322793 unintpropQ[n_]:=And[SameQ@@Last/@FactorInteger[n],FactorInteger[n][[1,2]]>1,Length[FactorInteger[n]]==PrimePi[FactorInteger[n][[-1,1]]]];
%t A322793 Select[Range[10000],unintpropQ]
%t A322793 (* Second program: *)
%t A322793 nn = 2^24; k = 1; P = 2; Union@ Reap[While[j = 2; While[P^j < nn, Sow[P^j]; j++]; j > 2, k++; P *= Prime[k]]][[-1, 1]] (* _Michael De Vlieger_, Oct 04 2023 *)
%Y A322793 Cf. A000961, A001597, A001694, A002110, A025487, A047966, A055932, A056239, A072774, A072777, A100778, A112798, A304250, A322792.
%K A322793 nonn
%O A322793 1,1
%A A322793 _Gus Wiseman_, Dec 26 2018