A240694 Partial products of divisors of n, cf. A027750.

1, 1, 2, 1, 3, 1, 2, 8, 1, 5, 1, 2, 6, 36, 1, 7, 1, 2, 8, 64, 1, 3, 27, 1, 2, 10, 100, 1, 11, 1, 2, 6, 24, 144, 1728, 1, 13, 1, 2, 14, 196, 1, 3, 15, 225, 1, 2, 8, 64, 1024, 1, 17, 1, 2, 6, 36, 324, 5832, 1, 19, 1, 2, 8, 40, 400, 8000, 1, 3, 21, 441, 1, 2

Offset: 1

Author

Reinhard Zumkeller, Apr 10 2014

Keywords

• nonn
• tabf

Comments

Triangle read by rows in which row n lists the partial products of divisors of n. - Omar E. Pol, Apr 12 2014

Examples

			.    n |  n-th row of A240694     |  n-th row of A027750
.  ----+--------------------------+---------------------
.    1 |  1                       |  1
.    2 |  1, 2                    |  1, 2
.    3 |  1, 3                    |  1, 3
.    4 |  1, 2, 8                 |  1, 2, 4
.    5 |  1, 5                    |  1, 5
.    6 |  1, 2, 6, 36             |  1, 2, 3, 6
.    7 |  1, 7                    |  1, 7
.    8 |  1, 2, 8, 64             |  1, 2, 4, 8
.    9 |  1, 3, 27                |  1, 3, 9
.   10 |  1, 2, 10, 100           |  1, 2, 5, 10
.   11 |  1, 11                   |  1, 11
.   12 |  1, 2, 6, 24, 144, 1728  |  1, 2, 3, 4, 6, 12
.   13 |  1, 13                   |  1, 13 .
		

Links

• Reinhard Zumkeller, Rows n = 1..1000 of table, flattened

Crossrefs

Cf. A000005 (row lengths), A007955, A020639, A027750, A240698.

Programs

Haskell

a240694 n k = a240694_tabf !! (n-1) !! (k-1)
a240694_row n = a240694_tabf !! (n-1)
a240694_tabf = map (scanl1 (*)) a027750_tabf

Mathematica

Table[FoldList[Times,Divisors[n]],{n,30}]//Flatten (* Harvey P. Dale, Jul 29 2021 *)

PARI

row(n) = my(d=divisors(n)); vector(#d, k, prod(i=1, k, d[i])); \\ Michel Marcus, Jan 24 2022

Formula

T(n,1) = 1, T(n,k) = T(n,k-1) * A027750(n,k), 1 < k <= n.

T(n,1) = 1;

T(n,2) = A020639(n), n > 1;

T(n,A000005(n)) = A007955(n);

T(n,A000005(n)-1) = A007956(n), n > 1.