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%I #10 Sep 15 2021 13:12:20
%S 1,1,2,1,1,2,1,3,3,3,1,1,1,1,2,1,2,4,4,4,4,1,1,1,1,1,1,2,1,4,4,4,4,4,
%T 4,4,1,1,3,3,3,3,3,3,3,1,2,2,2,4,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,2,1,3,
%U 6,6,6,6,6,6,6,6,6,6,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,4,4,4,4,4,4,4,4
%N Triangle T(n,k) = number of k-smooth divisors of n, read by rows.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.
%F T(n,n) = A000005(n);
%F T(n,2) = A001511(n) for n>1.
%F T(n,3) = A072078(n) for n>2.
%e Triangle begins:
%e 1
%e 1 2
%e 1 1 2
%e 1 3 3 3
%e 1 1 1 1 2
%e 1 2 4 4 4 4
%e 1 1 1 1 1 1 2
%e 1 4 4 4 4 4 4 4
%e 1 1 3 3 3 3 3 3 3
%t T[n_, k_] := Times@@(IntegerExponent[n, #]+1& /@ Select[Range[2, k], PrimeQ]);
%t Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 15 2021 *)
%Y Cf. A000005, A001511, A072078.
%K nonn,tabl
%O 1,3
%A _Reinhard Zumkeller_, Mar 14 2003
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