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%I #8 Sep 19 2021 08:05:17
%S 1,1,2,1,2,3,1,2,4,4,1,2,4,4,5,1,2,4,4,6,6,1,2,4,4,6,6,7,1,2,4,4,6,6,
%T 8,8,1,2,4,4,6,6,9,9,9,1,2,4,4,6,6,10,10,10,10,1,2,4,4,6,6,10,10,10,
%U 10,11,1,2,4,4,6,6,10,10,10,10,12,12,1,2,4,4,6,6,10,10,10,10,12,12,13,1,2,4,4
%N Numbers of numbers <= n having prime factors <= k, triangular array read by rows.
%C T(n,k) = #{m: 1<=m<=n and p<=k for prime factors of m}.
%F T(n, n)=n and T(n, k-1) = if k is prime then k-1 else T(n, k), 1<k<=n.
%e Triangle begins:
%e ................. 1
%e ............... 1...2
%e ............. 1...2...3
%e ........... 1...2...4...4
%e ......... 1...2...4...4...5
%e ....... 1...2...4...4...6...6
%e ..... 1...2...4...4...6...6...7
%e ... 1...2...4...4...6...6...8...8.
%t T[n_, k_] := T[n, k] = If[k == n, n, If[PrimeQ[k+1], k, T[n, k+1]]];
%t Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 19 2021 *)
%K nonn,tabl
%O 1,3
%A _Reinhard Zumkeller_, Mar 10 2003
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