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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). 6

%I

%S 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 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 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

%N 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 Row sums = A129235: (1, 4, 6, 11, 10, 20, 14,...). Moebius transform of A129234 = A129236. Inverse Moebius transform of A129234 = A129237.

%F G.f.=G(t,z)=Sum[t^k*z^k*[k-(k-1)z^k]/(1-z^k)^2, k=1..infinity). - _Emeric Deutsch_, Apr 17 2007

%e First few rows of the triangle are:

%e 1;

%e 2, 2;

%e 3, 0, 3;

%e 4, 3, 0, 4;

%e 5, 0, 0, 0, 5;

%e 6, 4, 4, 0, 0, 6;

%e 7, 0, 0, 0, 0, 0, 7;

%e ...

%p 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

%Y Cf. A129235, A129236, A129237.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Apr 05 2007

%E Edited by _Emeric Deutsch_, Apr 17 2007

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)