A342905 Array read by antidiagonals: T(n,k) = product of all distinct primes dividing n*k (n>=1, k>=1).

1, 2, 2, 3, 2, 3, 2, 6, 6, 2, 5, 2, 3, 2, 5, 6, 10, 6, 6, 10, 6, 7, 6, 15, 2, 15, 6, 7, 2, 14, 6, 10, 10, 6, 14, 2, 3, 2, 21, 6, 5, 6, 21, 2, 3, 10, 6, 6, 14, 30, 30, 14, 6, 6, 10, 11, 10, 3, 2, 35, 6, 35, 2, 3, 10, 11, 6, 22, 30, 6, 10, 42, 42, 10, 6, 30, 22, 6

Offset

1,2

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10011

Formula

T(n, k) = A007947(n * k).

Example

The array begins:
1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ...,
2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,
3, 6, 3, 6, 15, 6, 21, 6, 3, 30, ...,
2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,
5, 10, 15, 10, 5, 30, 35, 10, 15, 10, ...,
6, 6, 6, 6, 30, 6, 42, 6, 6, 30, ...,
7, 14, 21, 14, 35, 42, 7, 14, 21, 70, ...,
2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,
3, 6, 3, 6, 15, 6, 21, 6, 3, 30, ...,
10, 10, 30, 10, 10, 30, 70, 10, 30, 10, ...,
...,
The first few antidiagonals are:
1,
2, 2,
3, 2, 3,
2, 6, 6, 2,
5, 2, 3, 2, 5,
6, 10, 6, 6, 10, 6,
7, 6, 15, 2, 15, 6, 7,
2, 14, 6, 10, 10, 6, 14, 2,
3, 2, 21, 6, 5, 6, 21, 2, 3,
...

Prog

(PARI) T(n, k) = vecprod(factor(n*k)[, 1]~)

Crossrefs

A variant of the GCD array A003989 and the LCM array A003990.

Cf. A007947.

Sequence in context: A072380 A144910 A080330 * A356741 A152872 A350883

Adjacent sequences: A342902 A342903 A342904 * A342906 A342907 A342908

Keyword

nonn,look,tabl

Author

Rémy Sigrist and N. J. A. Sloane, Apr 02 2021

Status

approved