A372673 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where T(n,k) = phi(k*n) / phi(k).

1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 3, 4, 4, 1, 1, 2, 2, 4, 2, 1, 2, 2, 4, 4, 4, 6, 1, 1, 3, 2, 4, 3, 6, 4, 1, 2, 2, 4, 5, 4, 6, 8, 6, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 1, 2, 3, 4, 4, 6, 6, 8, 9, 8, 10, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 1, 2, 2, 4, 4, 4, 7, 8, 6, 8, 10, 8, 12, 1, 1, 3, 2, 5, 3, 6, 4, 9, 5, 10, 6, 12, 6

Offset

1,5

Links

Seiichi Manyama, Antidiagonals n = 1..140, flattened

Example

Square array T(n,k) begins:
  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
  1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
  2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, ...
  2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, ...
  4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 4, ...
  2, 4, 3, 4, 2, 6, 2, 4, 3, 4, 2, 6, 2, 4, 3, 4, 2, 6, ...
  6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, ...
  4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, ...
  6, 6, 9, 6, 6, 9, 6, 6, 9, 6, 6, 9, 6, 6, 9, 6, 6, 9, ...

Prog

(PARI) T(n, k) = eulerphi(k*n)/eulerphi(k);

Crossrefs

Columns k=1..18 give: A000010, A062570, A195459, A062570, A359101, A372671, A359102, A062570, A195459, A372672, A372676, A372671, A372677, A372678, A372679, A062570, A372681, A372671.

Main diagonal gives A000027.

Cf. A005117, A372619.

Sequence in context: A320473 A194884 A078401 * A271381 A086247 A116452

Adjacent sequences: A372670 A372671 A372672 * A372674 A372675 A372676

Keyword

nonn,tabl

Author

Seiichi Manyama, May 10 2024

Status

approved