A079548 Array T(m,n) = n*phi(m) - phi(mn) (m,n >= 1), read by antidiagonals.

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

Offset

1,8

Comments

It follows from the definition that n*phi(m) - 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..99.

Example

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

Mathematica

T[m_, n_] := n*EulerPhi[m] - 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, A079549, A079550.

Sequence in context: A089538 A152439 A070965 * A175620 A319812 A079071

Adjacent sequences: A079545 A079546 A079547 * A079549 A079550 A079551

Keyword

nonn,tabl,changed

Author

N. J. A. Sloane, Jan 24 2003

Status

approved