cp's OEIS Frontend

A177121 Square array T(n,k) read by antidiagonals up: T(n,k) = 1 if n=1; otherwise if n divides k then T(n,k) = -n+1; otherwise T(n,k) = 1.

%I A177121 #18 Jul 28 2019 21:03:24
%S A177121 1,1,1,1,-1,1,1,1,1,1,1,1,-2,-1,1,1,1,1,1,1,1,1,1,1,-3,1,-1,1,1,1,1,1,
%T A177121 1,-2,1,1,1,1,1,1,-4,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-5,1,-3,
%U A177121 -2,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-6,1,1,1,1,-1,1,1,1,1,1,1,1,1,1
%N A177121 Square array T(n,k) read by antidiagonals up: T(n,k) = 1 if n=1; otherwise if n divides k then T(n,k) = -n+1; otherwise T(n,k) = 1.
%C A177121 Replace the first column in A077049 with any k-th column in A177121 (this array) to get a new array. Then the matrix inverse of the new array will have the k-th column of A054535 (Ramanujan sum) as its first column.
%C A177121 Obtained from A176079 by transposing, flipping signs, and adding a lower triangle of all -1's. - _R. J. Mathar_, Jul 08 2011
%H A177121 Antti Karttunen, <a href="/A177121/b177121.txt">Table of n, a(n) for n = 1..65703 (the first 362 antidiagonals of array)</a>
%F A177121 T(n,k) = 1 if n=1; otherwise, if n divides k then T(n,k) = -n+1; otherwise T(n,k) = 1.
%e A177121 Table begins:
%e A177121   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
%e A177121   1, -1,  1, -1,  1, -1,  1, -1,  1, -1, ...
%e A177121   1,  1, -2,  1,  1, -2,  1,  1, -2,  1, ...
%e A177121   1,  1,  1, -3,  1,  1,  1, -3,  1,  1, ...
%e A177121   1,  1,  1,  1, -4,  1,  1,  1,  1, -4, ...
%e A177121   1,  1,  1,  1,  1, -5,  1,  1,  1,  1, ...
%e A177121   1,  1,  1,  1,  1,  1, -6,  1,  1,  1, ...
%e A177121   1,  1,  1,  1,  1,  1,  1, -7,  1,  1, ...
%e A177121   1,  1,  1,  1,  1,  1,  1,  1, -8,  1, ...
%e A177121   1,  1,  1,  1,  1,  1,  1,  1,  1, -9, ...
%e A177121   ...
%o A177121 (Excel) =if(row()=1;1;if(mod(column();row())=0;-row()+1;1))
%o A177121 (PARI)
%o A177121 up_to = 65703; \\ = binomial(362+1,2)
%o A177121 A177121sq(row,col) = if(1==row,1,if(!(col%row),(1-row),1));
%o A177121 A177121list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, if(i++ > up_to, return(v)); v[i] = A177121sq((a-(col-1)),col))); (v); };
%o A177121 v177121 = A177121list(up_to);
%o A177121 A177121(n) = v177121[n]; \\ _Antti Karttunen_, Sep 25 2018
%Y A177121 Cf. A051731, A054535, A077049, A176079.
%K A177121 sign,tabl,look
%O A177121 1,13
%A A177121 _Mats Granvik_ and _Gary W. Adamson_, May 03 2010