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

%I A342905 #21 Apr 03 2021 12:13:19
%S A342905 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 A342905 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 A342905 35,6,35,2,3,10,11,6,22,30,6,10,42,42,10,6,30,22,6
%N A342905 Array read by antidiagonals: T(n,k) = product of all distinct primes dividing n*k (n>=1, k>=1).
%H A342905 Rémy Sigrist, <a href="/A342905/b342905.txt">Table of n, a(n) for n = 1..10011</a>
%F A342905 T(n, k) = A007947(n * k).
%e A342905 The array begins:
%e A342905 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ...,
%e A342905 2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,
%e A342905 3, 6, 3, 6, 15, 6, 21, 6, 3, 30, ...,
%e A342905 2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,
%e A342905 5, 10, 15, 10, 5, 30, 35, 10, 15, 10, ...,
%e A342905 6, 6, 6, 6, 30, 6, 42, 6, 6, 30, ...,
%e A342905 7, 14, 21, 14, 35, 42, 7, 14, 21, 70, ...,
%e A342905 2, 2, 6, 2, 10, 6, 14, 2, 6, 10, ...,
%e A342905 3, 6, 3, 6, 15, 6, 21, 6, 3, 30, ...,
%e A342905 10, 10, 30, 10, 10, 30, 70, 10, 30, 10, ...,
%e A342905 ...,
%e A342905 The first few antidiagonals are:
%e A342905 1,
%e A342905 2, 2,
%e A342905 3, 2, 3,
%e A342905 2, 6, 6, 2,
%e A342905 5, 2, 3, 2, 5,
%e A342905 6, 10, 6, 6, 10, 6,
%e A342905 7, 6, 15, 2, 15, 6, 7,
%e A342905 2, 14, 6, 10, 10, 6, 14, 2,
%e A342905 3, 2, 21, 6, 5, 6, 21, 2, 3,
%e A342905 ...
%o A342905 (PARI) T(n, k) = vecprod(factor(n*k)[,1]~)
%Y A342905 A variant of the GCD array A003989 and the LCM array A003990.
%Y A342905 Cf. A007947.
%K A342905 nonn,look,tabl
%O A342905 1,2
%A A342905 _Rémy Sigrist_ and _N. J. A. Sloane_, Apr 02 2021