A079549 Array T(m,n) = m*phi(n) - phi(mn) (m,n >= 1), read by antidiagonals.

0, 1, 0, 1, 0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 4, 1, 4, 2, 4, 0, 1, 2, 2, 0, 4, 0, 0, 4, 1, 6, 2, 8, 0, 6, 0, 3, 0, 2, 4, 0, 0, 6, 0, 0, 6, 3, 8, 2, 16, 2, 12, 4, 6, 0, 1, 2, 0, 0, 4, 0, 6, 0, 0, 0, 0, 8, 1, 12, 6, 16, 2, 24, 4, 12, 4, 10, 0, 1, 4, 2, 4, 12, 0, 0, 8, 6, 0, 10, 0, 0, 8, 1, 12, 2, 20, 0, 24, 4, 18

Offset

1,7

Comments

It follows from the definition that m*phi(n) - phi(mn) >= 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..100.

Example

Array begins:
  m\n |  1    2    3    4    5    6 ...
  ----+--------------------------------
  1   |  0    1    1    2    1    4 ...
  2   |  0    0    1    0    1    2 ...
  3   |  0    2    0    4    2    6 ...
  4   |  0    0    2    0    2    4 ...
  5   |  0    4    4    8    0   16 ...
  6   |  0    0    0    0    2    0 ...
  ...

Mathematica

T[m_, n_] := m*EulerPhi[n] - EulerPhi[m*n]; Table[T[m, n - m + 1], {n, 1, 14}, {m, n, 1, -1}] // Flatten (* Amiram Eldar, Apr 23 2024 *)

Crossrefs

Cf. A000010, A076953, A079548, A079550.

Sequence in context: A317902 A317871 A082995 * A143374 A277899 A283760

Adjacent sequences: A079546 A079547 A079548 * A079550 A079551 A079552

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 24 2003

Status

approved