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

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, 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

Offset

0,5

Comments

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

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

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

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, 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;

Maple

with(numtheory) ;
A178085 := proc(n, m)
        1-phi(n)+phi(m)+phi(n-m) ;
end proc: # R. J. Mathar, Jul 14 2012

Mathematica

t[n_, m_, q_] := 1 - EulerPhi[n + q] + (EulerPhi[m + q] + EulerPhi[n - m + q]) - EulerPhi[q];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

Crossrefs

Sequence in context: A367760 A195007 A276947 * A078572 A122750 A329041

Adjacent sequences: A178082 A178083 A178084 * A178086 A178087 A178088

Keyword

sign,tabl,easy

Author

Roger L. Bagula, May 19 2010

Status

approved