A079550 Array T(m,n) = phi(m^2)*phi(n^2) - phi(m*n)^2 (m,n >= 1), read by antidiagonals.

0, 1, 1, 2, 0, 2, 4, 8, 8, 4, 4, 0, 0, 0, 4, 8, 24, 32, 32, 24, 8, 6, 8, 56, 0, 56, 8, 6, 16, 48, 36, 96, 96, 36, 48, 16, 18, 0, 108, 32, 0, 32, 108, 0, 18, 24, 72, 128, 192, 176, 176, 192, 128, 72, 24, 10, 16, 0, 0, 264, 0, 264, 0, 0, 16, 10, 32, 120, 176, 288, 384, 360, 360, 384, 288

Offset

1,4

Comments

It is known that phi(m^2)*phi(n^2) >= phi(m*n)^2.

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.2.2.

Links

Table of n, a(n) for n=1..75.

Example

Array begins:
  m\n |  1    2    3    4    5    6 ...
  ----+--------------------------------
  1   |  0    1    2    4    4    8 ...
  2   |  1    0    8    0   24    8 ...
  3   |  2    8    0   32   56   36 ...
  4   |  4    0   32    0   96   32 ...
  5   |  4   24   56   96    0  176 ...
  6   |  8    8   36   32  176    0 ...
  ...

Mathematica

T[m_, n_] := EulerPhi[m^2] * EulerPhi[n^2] - EulerPhi[m*n]^2; Table[T[m, n-m+1], {n, 1, 12}, {m, 1, n}] // Flatten (* Amiram Eldar, Apr 23 2024 *)

Crossrefs

Cf. A000010, A076953, A079548, A079549.

Sequence in context: A058210 A360860 A274414 * A226430 A067648 A279327

Adjacent sequences: A079547 A079548 A079549 * A079551 A079552 A079553

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 24 2003

Status

approved