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

%I #21 Apr 03 2021 12:13:19

%S 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,

%T 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,

%U 35,6,35,2,3,10,11,6,22,30,6,10,42,42,10,6,30,22,6

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

%H Rémy Sigrist, <a href="/A342905/b342905.txt">Table of n, a(n) for n = 1..10011</a>

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

%e The array begins:

%e 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ...,

%e 2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,

%e 3, 6, 3, 6, 15, 6, 21, 6, 3, 30, ...,

%e 2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,

%e 5, 10, 15, 10, 5, 30, 35, 10, 15, 10, ...,

%e 6, 6, 6, 6, 30, 6, 42, 6, 6, 30, ...,

%e 7, 14, 21, 14, 35, 42, 7, 14, 21, 70, ...,

%e 2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,

%e 3, 6, 3, 6, 15, 6, 21, 6, 3, 30, ...,

%e 10, 10, 30, 10, 10, 30, 70, 10, 30, 10, ...,

%e ...,

%e The first few antidiagonals are:

%e 1,

%e 2, 2,

%e 3, 2, 3,

%e 2, 6, 6, 2,

%e 5, 2, 3, 2, 5,

%e 6, 10, 6, 6, 10, 6,

%e 7, 6, 15, 2, 15, 6, 7,

%e 2, 14, 6, 10, 10, 6, 14, 2,

%e 3, 2, 21, 6, 5, 6, 21, 2, 3,

%e ...

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

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

%Y Cf. A007947.

%K nonn,look,tabl

%O 1,2

%A _Rémy Sigrist_ and _N. J. A. Sloane_, Apr 02 2021