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 A109626 #27 Jan 28 2025 00:58:39
%S A109626 1,1,1,1,2,1,1,3,1,1,1,4,3,2,1,1,5,2,1,2,1,1,6,5,4,3,2,1,1,7,3,5,3,3,
%T A109626 1,1,1,8,7,2,5,4,3,2,1,1,9,4,7,3,1,4,3,2,1,1,10,9,8,7,6,5,4,3,2,1,1,
%U A109626 11,5,3,2,7,6,5,1,3,1,1,1,12,11,10,9,8,7,6,5,4,3,2,1,1,13,6,11,10,9,4,1,3,5
%N A109626 Consider the array T(n,m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the antidiagonal read from lower left to upper right.
%H A109626 G. C. Greubel, <a href="/A109626/b109626.txt">Antidiagonals n = 1..100, flattened</a>
%F A109626 When m is prime, column m is T(n,m) = n/gcd(m, n) = numerator of n/(n+m). - _M. F. Hasler_, Jan 27 2025
%e A109626 Table begins:
%e A109626 \k...0...1...2...3...4...5...6...7...8...9..10..11..12..13
%e A109626 n\
%e A109626 1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A109626 2| 1 2 1 2 2 2 1 2 2 2 1 2 1 2
%e A109626 3| 1 3 3 1 3 3 3 3 3 3 3 3 1 3
%e A109626 4| 1 4 2 4 3 4 4 4 1 4 4 4 3 4
%e A109626 5| 1 5 5 5 5 1 5 5 5 5 4 5 5 5
%e A109626 6| 1 6 3 2 3 6 6 6 3 4 6 6 6 6
%e A109626 7| 1 7 7 7 7 7 7 1 7 7 7 7 7 7
%e A109626 8| 1 8 4 8 2 8 4 8 7 8 8 8 4 8
%e A109626 9| 1 9 9 3 9 9 3 9 9 1 9 9 6 9
%e A109626 10| 1 10 5 10 10 2 5 10 10 10 3 10 5 10
%e A109626 11| 1 11 11 11 11 11 11 11 11 11 11 1 11 11
%e A109626 12| 1 12 6 4 9 12 4 12 12 8 6 12 6 12
%e A109626 13| 1 13 13 13 13 13 13 13 13 13 13 13 13 1
%e A109626 14| 1 14 7 14 7 14 14 2 7 14 14 14 14 14
%e A109626 15| 1 15 15 5 15 3 10 15 15 10 15 15 5 15
%e A109626 16| 1 16 8 16 4 16 8 16 10 16 8 16 12 16
%t A109626 f[n_]:= f[n]= Block[{a}, a[0] = 1; a[l_]:= a[l]= Block[{k = 1, s = Sum[ a[i]*x^i, {i,0,l-1}]}, While[ IntegerQ[Last[CoefficientList[Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j,0,32}]];
%t A109626 T[n_, m_]:= f[n][[m]];
%t A109626 Flatten[Table[T[i,n-i], {n,15}, {i,n-1,1,-1}]]
%o A109626 (PARI) A109626_row(n, len=40)={my(A=1, m); vector(len, k, if(k>m=1, while(denominator(polcoeff(sqrtn(O(x^k)+A+=x^(k-1), n), k-1))>1, m++); m, 1))} \\ _M. F. Hasler_, Jan 27 2025
%Y A109626 Rows: A000012, A083952, A083953, A083954, A083945, A083946, A083947, A083948, A083949, A083950, A084066, A084067.
%Y A109626 Columns: A000012, A111627, A026741, A051176, A111607, A060791, A111608, A106608, A111609, A111610, A111611, A106612, A106614, A106618, A106620.
%Y A109626 Diagonals: A000027 (main), A111614 (first upper), A111627 (2nd), A111615 (3rd), A111618 (first lower), A111623 (2nd).
%Y A109626 Other diagonals: A005408 (T(2*n-1, n)), A111626, A111627, A111628, A111629, A111630.
%Y A109626 Cf. A111603, A111604.
%K A109626 nonn,tabl
%O A109626 1,5
%A A109626 _Paul D. Hanna_ and _Robert G. Wilson v_, Aug 01 2005