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A080772 Numbers of numbers <= n having prime factors <= k, triangular array read by rows. 0

%I

%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-Fran├žois Alcover_, Sep 19 2021 *)

%K nonn,tabl

%O 1,3

%A _Reinhard Zumkeller_, Mar 10 2003

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Last modified March 29 07:53 EDT 2023. Contains 361596 sequences. (Running on oeis4.)