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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 09:05 EST 2023. Contains 359838 sequences. (Running on oeis4.)