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 A234575 #37 Jun 01 2025 13:53:24
%S A234575 1,2,1,3,2,1,4,2,2,1,5,3,3,2,1,6,3,2,3,2,1,7,4,3,4,3,2,1,8,4,4,2,4,3,
%T A234575 2,1,9,5,3,3,5,4,3,2,1,10,5,4,4,2,5,4,3,2,1,11,6,5,5,3,6,5,4,3,2,1,12,
%U A234575 6,4,3,4,2,6,5,4,3,2,1,13,7,5,4,5,3,7,6,5
%N A234575 Triangle T(n, k) read by rows: T(n, k) = floor(n/k) + n mod k.
%H A234575 Antti Karttunen, <a href="/A234575/b234575.txt">Rows n = 1..144 of triangular table, flattened</a>
%F A234575 T(n, k) = A048158(n, k) + A010766(n, k). - _Reinhard Zumkeller_, Apr 29 2015
%F A234575 G.f. of the k-th column: x^k*((Sum_{i=0..k-1} x^i) - (k-1)*x^k)/((1 - x)^2*Sum_{i=0..k-1} x^i). - _Stefano Spezia_, May 08 2024
%F A234575 T(n, k) = n - (k - 1) * floor(n/k). - _Peter Luschny_, Jun 01 2025
%e A234575 Triangle begins:
%e A234575 1
%e A234575 2 1
%e A234575 3 2 1
%e A234575 4 2 2 1
%e A234575 5 3 3 2 1
%e A234575 6 3 2 3 2 1
%e A234575 7 4 3 4 3 2 1
%e A234575 8 4 4 2 4 3 2 1
%e A234575 9 5 3 3 5 4 3 2 1
%e A234575 10 5 4 4 2 5 4 3 2 1
%e A234575 11 6 5 5 3 6 5 4 3 2 1
%e A234575 12 6 4 3 4 2 6 5 4 3 2 1
%e A234575 13 7 5 4 5 3 7 6 5 4 3 2 1
%e A234575 14 7 6 5 6 4 2 7 6 5 4 3 2 1
%e A234575 15 8 5 6 3 5 3 8 7 6 5 4 3 2 1
%t A234575 With[{rows=10},Table[Floor[n/k]+Mod[n,k],{n,rows},{k,n}]] (* _Paolo Xausa_, Sep 26 2023 *)
%o A234575 (Python)
%o A234575 for n in range(1, 19):
%o A234575 for k in range(1, n+1):
%o A234575 c = n//k + n%k
%o A234575 print('%2d' % c, end=' ')
%o A234575 print()
%o A234575 (Python)
%o A234575 def T(n, k) -> int: return n - (k - 1) * (n // k)
%o A234575 for n in range(1,16): print([T(n, k) for k in range(1,n+1)]) # _Peter Luschny_, Jun 01 2025
%o A234575 (Scheme)
%o A234575 ;; MIT/GNU Scheme
%o A234575 (define (A234575bi n k) (+ (floor->exact (/ n k)) (modulo n k)))
%o A234575 (define (A234575 n) (A234575bi (A002024 n) (A002260 n)))
%o A234575 ;; _Antti Karttunen_, Dec 29 2013
%o A234575 (Haskell)
%o A234575 a234575 n k = a234575_tabl !! (n-1) !! (k-1)
%o A234575 a234575_row n = a234575_tabl !! (n-1)
%o A234575 a234575_tabl = zipWith (zipWith (+)) a048158_tabl a010766_tabl
%o A234575 -- _Reinhard Zumkeller_, Apr 29 2015
%Y A234575 Cf. A048158, A010766.
%K A234575 nonn,easy,tabl
%O A234575 1,2
%A A234575 _Alex Ratushnyak_, Dec 28 2013