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 A365656 #32 Jan 23 2024 16:18:49
%S A365656 1,2,4,3,8,9,5,16,27,25,6,32,81,125,12,7,64,243,625,18,49,10,128,729,
%T A365656 3125,24,343,20,11,256,2187,15625,36,2401,40,121,13,512,6561,78125,48,
%U A365656 16807,50,1331,169,14,1024,19683,390625,54,117649,80,14641,2197,28,15
%N A365656 Array T(n,k) read by antidiagonals (downward): T(n,1) = A005117(n) (squarefree numbers > 1); for k > 1, columns are nonsquarefree numbers (in descending order) with exactly the same prime factors as T(n,1).
%C A365656 Permutation of natural numbers.
%C A365656 Transpose of A284311 with a(0) = 1 prepended.
%C A365656 Essentially the same as A284457. - _R. J. Mathar_, Jan 23 2024
%H A365656 Michael De Vlieger, <a href="/A365656/b365656.txt">Table of n, a(n) for n = 0..11326</a> (rows 0..150, flattened)
%H A365656 Michael De Vlieger, <a href="/A365656/a365656.png">Log log scatterplot of log_10(a(n))</a>, n = 1..64981 (i.e., 360 rows, flattened).
%H A365656 Michael De Vlieger, <a href="/A365656/a365656_1.png">Log log scatterplot of log_10(a(n))</a>, n = 1..4096, showing primes in red, squarefree composites in green, composite prime powers in gold, and numbers neither squarefree nor prime powers in blue and purple; we show squareful numbers that are not prime powers in purple.
%F A365656 For prime n = p, T(p,k) = p^k.
%e A365656 Table T(n,k) for n = 1..12 and k = 1..6 shown below:
%e A365656 n\k | 1 2 3 4 5 6 ...
%e A365656 ----------------------------------------------
%e A365656 1 | 1
%e A365656 2 | 2 4 8 16 32 64
%e A365656 3 | 3 9 27 81 243 729
%e A365656 4 | 5 25 125 625 3125 15625
%e A365656 5 | 6 12 18 24 36 48
%e A365656 6 | 7 49 343 2401 16807 117649
%e A365656 7 | 10 20 40 50 80 100
%e A365656 8 | 11 121 1331 14641 161051 1771561
%e A365656 9 | 13 169 2197 28561 371293 4826809
%e A365656 10 | 14 28 56 98 112 196
%e A365656 11 | 15 45 75 135 225 375
%e A365656 12 | 17 289 4913 83521 1419857 24137569
%e A365656 ...
%e A365656 Triangle begins:
%e A365656 1;
%e A365656 2;
%e A365656 4, 3;
%e A365656 8, 9, 5;
%e A365656 16, 27, 25, 6;
%e A365656 32, 81, 125, 12, 7;
%e A365656 64, 243, 625, 18, 49, 10;
%e A365656 ...
%t A365656 f[n_, k_ : 1] := Block[{c = 0, s = Sign[k], m}, m = n + s;
%t A365656 While[c < Abs[k], While[! SquareFreeQ@ m, If[s < 0, m--, m++]];
%t A365656 If[s < 0, m--, m++]; c++];
%t A365656 m + If[s < 0, 1, -1] ] (* after Robert G.Wilson v at A005117 *);
%t A365656 T[n_, k_] := T[n, k] =
%t A365656 Which[And[n == 1, k == 1], 2, k == 1, f@T[n - 1, k],
%t A365656 PrimeQ@ T[n, 1], T[n, 1]^k, True,
%t A365656 Module[{j = T[n, k - 1]/T[n, 1] + 1},
%t A365656 While[PowerMod[T[n, 1], j, j] != 0, j++]; j T[n, 1]]]; {1}~Join~
%t A365656 Table[T[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // TableForm
%Y A365656 Cf. A002260, A005117, A007947, A065642, A284311, A284457.
%K A365656 nonn,tabf
%O A365656 0,2
%A A365656 _Michael De Vlieger_, Nov 17 2023