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

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}.

Links

Table of n, a(n) for n=1..95.

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

Adjacent sequences: A080769 A080770 A080771 * A080773 A080774 A080775

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Mar 10 2003

Status

approved