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 A386822 #33 Sep 05 2025 14:23:20
%S A386822 1,2,4,12,8,72,360,16,432,10800,75600,32,2592,324000,15876000,
%T A386822 174636000,64,15552,9720000,3333960000,403409160000,5244319080000,128,
%U A386822 93312,291600000,700131600000,931875159600000,157486901972400000,2677277333530800000
%N A386822 Irregular table T(n,k) = Product_{j = 1..k} prime(j)^(n-j+1), n >= 0, k = 1..n.
%C A386822 Proper subset of A025487, in turn a proper subset of A055932.
%C A386822 For n > 1, T(n,n) is in A332785.
%C A386822 For 1 < k < n, T(n,k) is in A286708, where A286708 is the sequence of powerful numbers (i.e., in A001694) that are not prime powers.
%C A386822 For n > 1 and k > 1, T(n,k) is in A126706.
%H A386822 Michael De Vlieger, <a href="/A386822/b386822.txt">Table of n, a(n) for n = 0..703</a> (rows n = 0..37, flattened.)
%F A386822 T(0,1) = 1 by convention.
%F A386822 T(n,1) = A000079(n) = 2^n.
%F A386822 T(n,n) = A006939(n).
%e A386822 Table begins:
%e A386822 n\k 1 2 3 4 5
%e A386822 ----------------------------------------------
%e A386822 0: 1;
%e A386822 1: 2;
%e A386822 2: 4, 12;
%e A386822 3: 8, 72, 360;
%e A386822 4: 16, 432, 10800, 75600;
%e A386822 5: 32, 2592, 324000, 15876000, 174636000;
%e A386822 Table of n, a(n) = P(k)^m * Q(k), for n < 12, illustrating prime power factor exponents, where k = omega(a(n)) = A001221(a(n)), P = A002110, and Q = A006939:
%e A386822 Exponents of
%e A386822 n a(n) k m 2.3.5.7
%e A386822 ---------------------------------------------------
%e A386822 1 1 .
%e A386822 2 2 = P(1)^0 * Q(1) 1 0 1
%e A386822 3 4 = P(1)^1 * Q(1) 1 1 2
%e A386822 4 12 = P(2)^0 * Q(2) 2 0 2.1
%e A386822 5 8 = P(1)^2 * Q(1) 1 2 3
%e A386822 6 72 = P(2)^1 * Q(2) 2 1 3.2
%e A386822 7 360 = P(3)^0 * Q(3) 3 0 3.2.1
%e A386822 8 16 = P(1)^3 * Q(1) 1 3 4
%e A386822 9 432 = P(2)^2 * Q(2) 2 2 4.3
%e A386822 10 10800 = P(3)^1 * Q(3) 3 1 4.3.2
%e A386822 11 75600 = P(4)^0 * Q(4) 4 0 4.3.2.1
%t A386822 Table[Product[Prime[j]^(n - j + 1), {j, k}], {n, 8}, {k, n}] // Flatten
%Y A386822 Cf. A000079, A001694, A006939, A025487, A055932, A126706, A286708, A332785, A387491.
%K A386822 nonn,tabf,easy,new
%O A386822 0,2
%A A386822 _Michael De Vlieger_, Aug 31 2025