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A076302 Triangle T(n,k) = number of k-smooth divisors of n, read by rows. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Sep 15 2021 *)

CROSSREFS

Cf. A000005, A001511, A072078.

Sequence in context: A239000 A105248 A289495 * A104524 A233322 A233324

Adjacent sequences:  A076299 A076300 A076301 * A076303 A076304 A076305

KEYWORD

nonn,tabl,changed

AUTHOR

Reinhard Zumkeller, Mar 14 2003

STATUS

approved

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Last modified September 25 12:38 EDT 2021. Contains 347654 sequences. (Running on oeis4.)