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 A258197 #31 Apr 13 2025 03:15:43
%S A258197 0,0,0,0,1,0,0,1,1,0,0,4,5,4,0,0,1,7,7,1,0,0,5,8,24,8,5,0,0,1,10,12,
%T A258197 12,10,1,0,0,12,32,92,59,92,32,12,0,0,6,60,124,165,165,124,60,6,0,0,7,
%U A258197 39,244,247,456,247,244,39,7,0,0,1,16,103,371,493,493,371,103,16,1,0
%N A258197 Arithmetic derivative of Pascal's triangle.
%C A258197 A258318(n) = number of distinct terms up to row n.
%H A258197 Reinhard Zumkeller, <a href="/A258197/b258197.txt">Rows n = 0..125 of triangle, flattened</a>
%F A258197 T(n,k) = A003415(A007318(n,k)), 0 <= k <= n.
%F A258197 For n > 0: T(n,1) = A003415(n).
%F A258197 For n > 1: T(n,2) = A068312(n-1).
%e A258197 . First 10 rows: | Pascal's triangle:
%e A258197 . 0: 0 | 1
%e A258197 . 1: 0,0 | 1,1
%e A258197 . 2: 0,1,0 | 1,2,1
%e A258197 . 3: 0,1,1,0 | 1,3,3,1
%e A258197 . 4: 0,4,5,4,0 | 1,4,6,4,1
%e A258197 . 5: 0,1,7,7,1,0 | 1,5,10,10,5,1
%e A258197 . 6: 0,5,8,24,8,5,0 | 1,6,15,20,15,6,1
%e A258197 . 7: 0,1,10,12,12,10,1,0 | 1,7,21,35,35,21,7,1
%e A258197 . 8: 0,12,32,92,59,92,32,12,0 | 1,8,28,56,70,56,28,8,1
%e A258197 . 9: 0,6,60,124,165,165,124,60,6,0 | 1,9,36,84,126,126,84,36,9,1 .
%t A258197 ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad[0] = ad[1] = 0; Table[ad[Binomial[n, k]], {n, 0, 11}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Apr 13 2025 *)
%o A258197 (Haskell)
%o A258197 a258197 n k = a258197_tabl !! n !! k
%o A258197 a258197_row n = a258197_tabl !! n
%o A258197 a258197_tabl = map (map a003415) a007318_tabl
%Y A258197 Cf. A003415, A007318, A258290 (central terms), A258317 (row sums), A068312, A258318.
%K A258197 nonn,tabl
%O A258197 0,12
%A A258197 _Reinhard Zumkeller_, May 26 2015