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A080772
Numbers of numbers <= n having prime factors <= k, triangular array read by rows.
0
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, 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, 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
OFFSET
1,3
COMMENTS
T(n,k) = #{m: 1<=m<=n and p<=k for prime factors of m}.
FORMULA
T(n, n)=n and T(n, k-1) = if k is prime then k-1 else T(n, k), 1<k<=n.
EXAMPLE
Triangle begins:
................. 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...8...8.
MATHEMATICA
T[n_, k_] := T[n, k] = If[k == n, n, If[PrimeQ[k+1], k, T[n, k+1]]];
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 19 2021 *)
CROSSREFS
Sequence in context: A194914 A195076 A163491 * A259324 A216274 A145111
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Mar 10 2003
STATUS
approved