cp's OEIS Frontend

A129234 Triangle read by rows: T(n,k) = n/k + k - 1 if n mod k = 0; otherwise T(n,k)=0 (1 <= k <= n).

%I A129234 #11 Jan 17 2025 09:09:35
%S A129234 1,2,2,3,0,3,4,3,0,4,5,0,0,0,5,6,4,4,0,0,6,7,0,0,0,0,0,7,8,5,0,5,0,0,
%T A129234 0,8,9,0,5,0,0,0,0,0,9,10,6,0,0,6,0,0,0,0,10,11,0,0,0,0,0,0,0,0,0,11,
%U A129234 12,7,6,6,0,7,0,0,0,0,0,12,13,0,0,0,0,0,0,0,0,0,0,0,13,14,8,0,0,0,0,8,0,0,0,0,0,0,14
%N A129234 Triangle read by rows: T(n,k) = n/k + k - 1 if n mod k = 0; otherwise T(n,k)=0 (1 <= k <= n).
%C A129234 Row sums = A129235: (1, 4, 6, 11, 10, 20, 14, ...). Moebius transform of A129234 = A129236. Inverse Moebius transform of A129234 = A129237.
%F A129234 G.f. = G(t,z) = Sum_{k>=1} t^k*z^k*(k-(k-1)*z^k)/(1-z^k)^2. - _Emeric Deutsch_, Apr 17 2007
%e A129234 First few rows of the triangle:
%e A129234   1;
%e A129234   2, 2;
%e A129234   3, 0, 3;
%e A129234   4, 3, 0, 4;
%e A129234   5, 0, 0, 0, 5;
%e A129234   6, 4, 4, 0, 0, 6;
%e A129234   7, 0, 0, 0, 0, 0, 7;
%e A129234   ...
%p A129234 T:=proc(n,k) if n mod k = 0 then n/k+k-1 else 0 fi end: for n from 1 to 16 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form - _Emeric Deutsch_, Apr 17 2007
%t A129234 T[n_,k_]:=If[Mod[n,k]==0,n/k+k-1,0];Table[T[n,k],{n,14},{k,n}]//Flatten (* _James C. McMahon_, Jan 17 2025 *)
%o A129234 (PARI) row(n) = vector(n, k, if (!(n%k), n/k + k - 1, 0)); \\ _Michel Marcus_, Jan 17 2025
%Y A129234 Cf. A129235, A129236, A129237.
%K A129234 nonn,tabl
%O A129234 1,2
%A A129234 _Gary W. Adamson_, Apr 05 2007
%E A129234 Edited by _Emeric Deutsch_, Apr 17 2007