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 A364878 #21 Aug 13 2023 02:46:49
%S A364878 1,4,2,36,12,6,900,180,60,30,44100,6300,1260,420,210,5336100,485100,
%T A364878 69300,13860,4620,2310,901800900,69369300,6306300,900900,180180,60060,
%U A364878 30030,260620460100,15330615300,1179278100,107207100,15315300,3063060,1021020,510510
%N A364878 Triangle read by rows: T(n,k), 0 <= k <= n, is the smallest number that has n distinct prime factors, k of which are unique.
%C A364878 If a number's prime factorization is written as the product of the number's prime factors without using exponents (e.g., 1260 = 2*2*3*3*5*7), a prime factor is unique (i.e., one of a kind) if it appears only once; prime factors that have one or more duplicates are not unique. E.g., the distinct prime factors of 1260 are 2, 3, 5, and 7, but the only unique prime factors of 1260 are 5 and 7.
%C A364878 From _Michael De Vlieger_, Aug 12 2023: (Start)
%C A364878 T(n,k) is in A025487 by definition.
%C A364878 The number 2 is the only prime term and 4 the only composite prime power term.
%C A364878 T(n,k), k < n, n > 2 is neither squarefree nor a prime power and is in A126706.
%C A364878 No prime power divisor p^e | T(n,k) is such that e > 2. (End)
%H A364878 Michael De Vlieger, <a href="/A364878/b364878.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150, flattened)
%F A364878 T(n,k) = Product_{j=1..n} prime(j)^m where m = 1 if j > n - k, m = 2 otherwise.
%F A364878 T(n,k) = A002110(n)*A002110(n-k).
%F A364878 T(n,n) = A002110(n).
%F A364878 T(n,0) = A002110(n)^2.
%e A364878 T(2,0) = 36: 36 = 2*2*3*3, so 36 has 2 distinct prime factors (2 and 3) but no unique prime factors (each prime factor has a duplicate), and 36 is the smallest number with this property.
%e A364878 T(2,2) = 6: 6 = 2*3, so 6 has 2 distinct prime factors (2 and 3), and each of those is a unique prime factor (having no duplicates), and 6 is the smallest number with this property.
%e A364878 T(3,2) = 60: 60 = 2*2*3*5, so 60 has 3 distinct prime factors (2, 3, and 5), but only 2 unique prime factors (3 and 5, since the factor 2 is duplicated), and 60 is the smallest number having this property.
%e A364878 Table begins:
%e A364878 n\k| 0 1 2 3 4 5 6
%e A364878 ---+-----------------------------------------------------------
%e A364878 0 | 1;
%e A364878 1 | 4, 2;
%e A364878 2 | 36, 12, 6;
%e A364878 3 | 900, 180, 60, 30;
%e A364878 4 | 44100, 6300, 1260, 420, 210;
%e A364878 5 | 5336100, 485100, 69300, 13860, 4620, 2310;
%e A364878 6 | 901800900, 69369300, 6306300, 900900, 180180, 60060, 30030;
%e A364878 ...
%t A364878 T[n_,k_]:=Module[{primes=Array[Prime,n],primeProducts},primeProducts=Table[If[j>n-k,primes[[j]],primes[[j]]^2],{j,1,n}];Times@@primeProducts];lst[rows_]:=Table[T[n,k],{n,0,rows},{k,0,n}]//Flatten;lst[7] (* _Robert P. P. McKone_, Aug 12 2023 *)
%Y A364878 Cf. A002110, A025487, A061742, A088860, A126706, A228593.
%K A364878 nonn,tabl
%O A364878 0,2
%A A364878 _Jon E. Schoenfield_, Aug 11 2023