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

2, 4, 12, 24, 72, 240, 720, 1440, 7200, 20160, 60480, 201600, 604800, 1693440, 13305600, 26611200, 79833600, 372556800, 1117670400, 3512678400, 20756736000, 58118860800, 174356582400, 581188608000, 2739889152000, 7671689625600, 45332711424000, 118562476032000

Offset: 1

Author

Michael De Vlieger, Oct 29 2021

Keywords

• nonn
• easy

Comments

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.

All terms are even.

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.

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

Examples

			a(1) = 2 since row n=1 of A237591 = {1}; prime(1)^1 = 2^1 = 2.
a(2) = 4 since row n=2 of A237591 = {2}; prime(1)^2 = 2^2 = 4.
a(3) = 12 since row n=3 of A237591 = {2,1}; prime(1)^2 * prime(2)^1 = 2^2 * 3^1 = 12, etc.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1594
• Michael De Vlieger, Log-log scatterplot of a(n) for n=1..2^16.

Crossrefs

Cf. A055932, A067255, A237591, A237593.

Programs

Mathematica

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}]