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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-François 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.)