A076953 Array T(m,n) = phi(mn)-phi(m)phi(n) (m,n >= 1), read by antidiagonals.

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.

Links

Table of n, a(n) for n=1..105.

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

Cf. A000010, A079548, A079549, A079550.

Sequence in context: A016414 A049337 A049801 * A180472 A308583 A093315

Adjacent sequences: A076950 A076951 A076952 * A076954 A076955 A076956

Keyword

nonn,tabl,changed

Author

N. J. A. Sloane, Jan 24 2003

Status

approved