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A178085 Triangle t(n,m) = 1 - phi(n) + phi(m) + phi(n - m) read by rows, 0<=m<=n. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
sign,tabl,easy
AUTHOR
Roger L. Bagula, May 19 2010
STATUS
approved

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)