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A348642 a(n) = Product_{k=1..A003056(n)} prime(k)^T(n,k), with row n of T = row n of A237591.

%I A348642 #10 Dec 18 2021 23:32:19
%S A348642 2,4,12,24,72,240,720,1440,7200,20160,60480,201600,604800,1693440,
%T A348642 13305600,26611200,79833600,372556800,1117670400,3512678400,
%U A348642 20756736000,58118860800,174356582400,581188608000,2739889152000,7671689625600,45332711424000,118562476032000
%N A348642 a(n) = Product_{k=1..A003056(n)} prime(k)^T(n,k), with row n of T = row n of A237591.
%C A348642 Compactification of row n of A237591 via product of prime powers. Row n of A237591 is interpreted instead as row n of A067255, returning index n from that sequence.
%C A348642 All terms are even.
%C A348642 Subset of A055932, but not a subset of A025487, since row n = 14 of A237591 is {8,3,1,2}. It is the least n such that at least one pair of terms in the row exhibit increase.
%C A348642 Intersection with A002182 = {2, 4, 12, 24, 240, 720, 20160} and is finite on account of the prime shape of a(n).
%H A348642 Michael De Vlieger, <a href="/A348642/b348642.txt">Table of n, a(n) for n = 1..1594</a>
%H A348642 Michael De Vlieger, <a href="/A348642/a348642.png">Log-log scatterplot of a(n)</a> for n=1..2^16.
%e A348642 a(1) = 2 since row n=1 of A237591 = {1}; prime(1)^1 = 2^1 = 2.
%e A348642 a(2) = 4 since row n=2 of A237591 = {2}; prime(1)^2 = 2^2 = 4.
%e A348642 a(3) = 12 since row n=3 of A237591 = {2,1}; prime(1)^2 * prime(2)^1 = 2^2 * 3^1 = 12, etc.
%t A348642 Table[Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, #] &@ Array[(Ceiling[(n + 1)/# - (# + 1)/2] - Ceiling[(n + 1)/(# + 1) - (# + 2)/2]) &, Floor[(Sqrt[8 n + 1] - 1)/2]], {n, 28}]
%Y A348642 Cf. A055932, A067255, A237591, A237593.
%K A348642 nonn,easy
%O A348642 1,1
%A A348642 _Michael De Vlieger_, Oct 29 2021