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Triangle read by rows, 1<=k<=n: T(n,k) = smallest number having exactly as many divisors as n and k together.
0

%I #9 Sep 15 2021 05:43:46

%S 2,4,6,4,6,6,6,16,16,12,4,6,6,16,6,16,12,12,64,12,24,4,6,6,16,6,12,6,

%T 16,12,12,64,12,24,12,24,6,16,16,12,16,64,16,64,12,16,12,12,64,12,24,

%U 12,24,64,24,4,6,6,16,6,12,6,12,16,12,6,64,24,24,36,24,48,24,48,36,48,24,60,4

%N Triangle read by rows, 1<=k<=n: T(n,k) = smallest number having exactly as many divisors as n and k together.

%F T(n,k) = A005179(A000005(n)+A000005(k)).

%e Triangle begins:

%e 2

%e 4 6

%e 4 6 6

%e 6 16 16 12

%e 4 6 6 16 6

%e ...

%t A005179 = Cases[Import["https://oeis.org/A005179/b005179.txt", "Table"], {_, _}][[All, 2]];

%t T[n_, k_] := A005179[[DivisorSigma[0, n] + DivisorSigma[0, k]]];

%t Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 15 2021 *)

%o (PARI) T(n,k) = my(x=numdiv(n)+numdiv(k), y=1); while(numdiv(y)!= x, y++); y; \\ _Michel Marcus_, Sep 15 2021

%Y Cf. A000005, A005179.

%K nonn,tabl

%O 1,1

%A _Reinhard Zumkeller_, Oct 31 2004