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A176079 Triangle T(n,k) read by rows: If k divides n then k-1, otherwise -1.

%I A176079 #23 Sep 08 2022 08:45:52
%S A176079 0,0,1,0,-1,2,0,1,-1,3,0,-1,-1,-1,4,0,1,2,-1,-1,5,0,-1,-1,-1,-1,-1,6,
%T A176079 0,1,-1,3,-1,-1,-1,7,0,-1,2,-1,-1,-1,-1,-1,8,0,1,-1,-1,4,-1,-1,-1,-1,
%U A176079 9,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,10,0,1,2,3,-1,5,-1,-1,-1,-1,-1,11
%N A176079 Triangle T(n,k) read by rows: If k divides n then k-1, otherwise -1.
%H A176079 G. C. Greubel, <a href="/A176079/b176079.txt">Rows n = 1..100 of triangle, flattened</a>
%F A176079 T(n,k) = -A191904(n,k) for n >= k.
%F A176079 Sum_{k=1..n} T(n,k) = A001065(n). - _Jon E. Schoenfield_, Nov 29 2019
%e A176079 Table begins:
%e A176079   0;
%e A176079   0,  1;
%e A176079   0, -1,  2;
%e A176079   0,  1, -1,  3;
%e A176079   0, -1, -1, -1,  4;
%e A176079   0,  1,  2, -1, -1,  5;
%e A176079   0, -1, -1, -1, -1, -1,  6;
%e A176079   0,  1, -1,  3, -1, -1, -1,  7;
%e A176079   0, -1,  2, -1, -1, -1, -1, -1,  8;
%e A176079   0,  1, -1, -1,  4, -1, -1, -1, -1, 9;
%p A176079 seq(seq( `if`(mod(n,k)=0, k-1, -1) , k=1..n), n=1..15); # _G. C. Greubel_, Nov 27 2019
%t A176079 Table[If[Divisible[n,k],k-1,-1],{n,15},{k,n}]//Flatten (* _Harvey P. Dale_, May 20 2016 *)
%o A176079 (PARI) T(n,k)= if(Mod(n,k)==0, k-1, -1); \\ _G. C. Greubel_, Nov 27 2019
%o A176079 (Magma) [(n mod k) eq 0 select k-1 else -1: k in [1..n], n in [1..15]]; // _G. C. Greubel_, Nov 27 2019
%o A176079 (Sage)
%o A176079 def T(n, k):
%o A176079     if (mod(n,k)==0): return k-1
%o A176079     else: return -1
%o A176079 [[T(n, k) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Nov 27 2019
%o A176079 (GAP)
%o A176079 T:= function(n,k)
%o A176079     if (n mod k = 0) then return k-1;
%o A176079     else return -1;
%o A176079     fi; end;
%o A176079 Flat(List([1..15], n-> List([1..n], k-> T(n,k) ))); # _G. C. Greubel_, Nov 27 2019
%Y A176079 Cf. A001065 (row sums), A191904.
%K A176079 sign,tabl
%O A176079 1,6
%A A176079 _Mats Granvik_, Apr 08 2010