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

1,3

Comments

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

Links

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

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.

Example

.    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 .

Mathematica

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

Prog

(Haskell)
a240694 n k = a240694_tabf !! (n-1) !! (k-1)
a240694_row n = a240694_tabf !! (n-1)
a240694_tabf = map (scanl1 (*)) a027750_tabf
(PARI) row(n) = my(d=divisors(n)); vector(#d, k, prod(i=1, k, d[i])); \\ Michel Marcus, Jan 24 2022

Crossrefs

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

Sequence in context: A293980 A365785 A368759 * A258643 A287561 A046924

Adjacent sequences: A240691 A240692 A240693 * A240695 A240696 A240697

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Apr 10 2014

Status

approved