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A076953
Array T(m,n) = phi(mn)-phi(m)phi(n) (m,n >= 1), read by antidiagonals.
3
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 8, 0, 8, 0, 8, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 8, 6, 8, 0, 8, 0, 4, 0, 0, 0, 4, 0, 4, 6, 0, 0, 6, 4, 0, 4, 0, 0
OFFSET
1,12
COMMENTS
It follows from the definition that phi(mn)-phi(m)phi(n) >= 0.
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter I, p. 9, section I.2.1.
EXAMPLE
Array begins:
m\n | 1 2 3 4 5 6 ...
----+--------------------------------
1 | 0 0 0 0 0 0 ...
2 | 0 1 0 2 0 2 ...
3 | 0 0 2 0 0 2 ...
4 | 0 2 0 4 0 0 ...
5 | 0 0 0 0 4 0 ...
6 | 0 2 2 4 0 8 ...
...
MATHEMATICA
T[m_, n_] := EulerPhi[m*n] - EulerPhi[m] * EulerPhi[n]; Table[T[m, n-m+1], {n, 1, 14}, {m, 1, n}] // Flatten (* Amiram Eldar, Apr 23 2024 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 24 2003
STATUS
approved