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 A178085 Triangle t(n,m) = 1 - phi(n) + phi(m) + phi(n - m) read by rows, 0<=m<=n. 1

%I

%S 1,1,1,1,2,1,1,1,1,1,1,2,1,2,1,1,0,0,0,0,1,1,4,2,3,2,4,1,1,-2,0,-1,-1,

%T 0,-2,1,1,4,0,3,1,3,0,4,1,1,0,2,-1,1,1,-1,2,0,1,1,4,2,5,1,5,1,5,2,4,1

%N Triangle t(n,m) = 1 - phi(n) + phi(m) + phi(n - m) read by rows, 0<=m<=n.

%C phi(.) is Euler's totient A000010(.).

%C Row sums are 1, 2, 4, 4, 7, 2, 17, -4, 17, 6, 31,... = (n+1)*(1-phi(n))+2*A002088(n).

%F t(n,m) = t(n,n-m).

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 1, 1, 1;

%e 1, 2, 1, 2, 1;

%e 1, 0, 0, 0, 0, 1;

%e 1, 4, 2, 3, 2, 4, 1;

%e 1, -2, 0, -1, -1, 0, -2, 1;

%e 1, 4, 0, 3, 1, 3, 0, 4, 1;

%e 1, 0, 2, -1, 1, 1, -1, 2, 0, 1;

%e 1, 4, 2, 5, 1, 5, 1, 5, 2, 4, 1;

%p with(numtheory) ;

%p A178085 := proc(n,m)

%p 1-phi(n)+phi(m)+phi(n-m) ;

%p end proc: # _R. J. Mathar_, Jul 14 2012

%t t[n_, m_, q_] := 1 - EulerPhi[n + q] + (EulerPhi[m + q] + EulerPhi[n - m + q]) - EulerPhi[q];

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

%K sign,tabl,easy

%O 0,5

%A _Roger L. Bagula_, May 19 2010

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Last modified August 8 10:26 EDT 2022. Contains 356009 sequences. (Running on oeis4.)