OFFSET
1,3
COMMENTS
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...7...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
(Python)
from itertools import count, islice
from sympy import prevprime, integer_log
def A080786_T(n, k):
if k==1: return 1
def g(x, m): return x.bit_length() if m==2 else sum(g(x//(m**i), prevprime(m))for i in range(integer_log(x, m)[0]+1))
return g(n, prevprime(k+1))
def A080786_gen(): # generator of terms
return (A080786_T(n, k) for n in count(1) for k in range(1, n+1))
CROSSREFS
KEYWORD
AUTHOR
Reinhard Zumkeller, Mar 12 2003
STATUS
approved