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A080786 Triangle T(n,k) = number of k-smooth numbers <= n, read by rows. 2
1, 1, 2, 1, 2, 3, 1, 3, 4, 4, 1, 3, 4, 4, 5, 1, 3, 5, 5, 6, 6, 1, 3, 5, 5, 6, 6, 7, 1, 4, 6, 6, 7, 7, 8, 8, 1, 4, 7, 7, 8, 8, 9, 9, 9, 1, 4, 7, 7, 9, 9, 10, 10, 10, 10, 1, 4, 7, 7, 9, 9, 10, 10, 10, 10, 11, 1, 4, 8, 8, 10, 10, 11, 11, 11, 11, 12, 12, 1, 4, 8, 8, 10, 10, 11, 11, 11, 11, 12, 12, 13, 1, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

T(n,n-1) = A014684(n) for n>1;

T(n,2) = A029837(n) for n>1; T(n,3) = A071521(n) for n>2; T(n,5) = A071520(n) for n>4.

A036234(n) = number of distinct terms in n-th row. - Reinhard Zumkeller, Sep 17 2013

LINKS

Reinhard Zumkeller, Rows n=1..120 of triangle, flattened

Eric Weisstein's World of Mathematics, Smooth Number.

EXAMPLE

Triangle begins:

.................. 1

................ 1...2

.............. 1...2...3

............ 1...3...4...4

.......... 1...3...4...4...5

........ 1...3...5...5...6...6

...... 1...3...5...5...6...6...7

.... 1...4...6...6...7...8...8...8

.. 1...4...7...7...8...8...9...9...9.

MAPLE

A080786 := proc(x, y)

    local a, n ;

    a := 0 ;

    for n from 1 to x do

        if A006530(n) <= y then

            a := a+1 ;

        end if;

    end do:

    a ;

end proc: # R. J. Mathar, Aug 31 2013

MATHEMATICA

P[n_] := FactorInteger[n][[-1, 1]]; P[1]=1; T[n_, k_] := (For[j=0; m=1, m <= n, m++, If[P[m] <= k, j++]]; j); Table[T[n, k], {n, 1, 15}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Nov 22 2015 *)

PROG

(Haskell)

a080786 n k = a080786_tabl !! (n-1) !! (k-1)

a080786_row n = a080786_tabl !! (n-1)

a080786_tabl = map reverse $ iterate f [1] where

   f xs@(x:_) = (x + 1) :

                (zipWith (+) xs (map (fromEnum . (lpf <=)) [x, x-1 ..]))

        where lpf = fromInteger $ a006530 $ fromIntegral (x + 1)

-- Reinhard Zumkeller, Sep 17 2013

CROSSREFS

Cf. A000079, A002473, A003586, A006530, A014684, A029837, A036234, A051037, A051038, A071520, A071521, A080197, A080681, A080682, A080683.

Sequence in context: A344088 A292595 A269596 * A036838 A066010 A209556

Adjacent sequences:  A080783 A080784 A080785 * A080787 A080788 A080789

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Mar 12 2003

STATUS

approved

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Last modified September 20 05:17 EDT 2021. Contains 347577 sequences. (Running on oeis4.)