A076302 Triangle T(n,k) = number of k-smooth divisors of n, read by rows.

1, 1, 2, 1, 1, 2, 1, 3, 3, 3, 1, 1, 1, 1, 2, 1, 2, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 2, 1, 4, 4, 4, 4, 4, 4, 4, 1, 1, 3, 3, 3, 3, 3, 3, 3, 1, 2, 2, 2, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Divisor Function.

Eric Weisstein's World of Mathematics, Smooth Number.

Formula

T(n,n) = A000005(n);

T(n,2) = A001511(n) for n>1.

T(n,3) = A072078(n) for n>2.

Example

Triangle begins:
                   1
                 1   2
               1   1   2
             1   3   3   3
           1   1   1   1   2
         1   2   4   4   4   4
       1   1   1   1   1   1   2
     1   4   4   4   4   4   4   4
   1   1   3   3   3   3   3   3   3

Mathematica

T[n_, k_] := Times@@(IntegerExponent[n, #]+1& /@ Select[Range[2, k], PrimeQ]);
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 15 2021 *)

Crossrefs

Cf. A000005, A001511, A072078.

Sequence in context: A105248 A377319 A289495 * A104524 A233322 A233324

Adjacent sequences: A076299 A076300 A076301 * A076303 A076304 A076305

Keyword

nonn,tabl,changed

Author

Reinhard Zumkeller, Mar 14 2003

Status

approved