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

%I #10 Dec 18 2021 23:32:19

%S 2,4,12,24,72,240,720,1440,7200,20160,60480,201600,604800,1693440,

%T 13305600,26611200,79833600,372556800,1117670400,3512678400,

%U 20756736000,58118860800,174356582400,581188608000,2739889152000,7671689625600,45332711424000,118562476032000

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

%C 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 All terms are even.

%C 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 Intersection with A002182 = {2, 4, 12, 24, 240, 720, 20160} and is finite on account of the prime shape of a(n).

%H Michael De Vlieger, <a href="/A348642/b348642.txt">Table of n, a(n) for n = 1..1594</a>

%H Michael De Vlieger, <a href="/A348642/a348642.png">Log-log scatterplot of a(n)</a> for n=1..2^16.

%e a(1) = 2 since row n=1 of A237591 = {1}; prime(1)^1 = 2^1 = 2.

%e a(2) = 4 since row n=2 of A237591 = {2}; prime(1)^2 = 2^2 = 4.

%e a(3) = 12 since row n=3 of A237591 = {2,1}; prime(1)^2 * prime(2)^1 = 2^2 * 3^1 = 12, etc.

%t 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 Cf. A055932, A067255, A237591, A237593.

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Oct 29 2021