cp's OEIS Frontend

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

%I A240694 #12 Jan 24 2022 09:58:10
%S A240694 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,
%T A240694 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,
%U A240694 324,5832,1,19,1,2,8,40,400,8000,1,3,21,441,1,2
%N A240694 Partial products of divisors of n, cf. A027750.
%C A240694 Triangle read by rows in which row n lists the partial products of divisors of n. - _Omar E. Pol_, Apr 12 2014
%H A240694 Reinhard Zumkeller, <a href="/A240694/b240694.txt">Rows n = 1..1000 of table, flattened</a>
%F A240694 T(n,1) = 1, T(n,k) = T(n,k-1) * A027750(n,k), 1 < k <= n.
%F A240694 T(n,1) = 1;
%F A240694 T(n,2) = A020639(n), n > 1;
%F A240694 T(n,A000005(n)) = A007955(n);
%F A240694 T(n,A000005(n)-1) = A007956(n), n > 1.
%e A240694 .    n |  n-th row of A240694     |  n-th row of A027750
%e A240694 .  ----+--------------------------+---------------------
%e A240694 .    1 |  1                       |  1
%e A240694 .    2 |  1, 2                    |  1, 2
%e A240694 .    3 |  1, 3                    |  1, 3
%e A240694 .    4 |  1, 2, 8                 |  1, 2, 4
%e A240694 .    5 |  1, 5                    |  1, 5
%e A240694 .    6 |  1, 2, 6, 36             |  1, 2, 3, 6
%e A240694 .    7 |  1, 7                    |  1, 7
%e A240694 .    8 |  1, 2, 8, 64             |  1, 2, 4, 8
%e A240694 .    9 |  1, 3, 27                |  1, 3, 9
%e A240694 .   10 |  1, 2, 10, 100           |  1, 2, 5, 10
%e A240694 .   11 |  1, 11                   |  1, 11
%e A240694 .   12 |  1, 2, 6, 24, 144, 1728  |  1, 2, 3, 4, 6, 12
%e A240694 .   13 |  1, 13                   |  1, 13 .
%t A240694 Table[FoldList[Times,Divisors[n]],{n,30}]//Flatten (* _Harvey P. Dale_, Jul 29 2021 *)
%o A240694 (Haskell)
%o A240694 a240694 n k = a240694_tabf !! (n-1) !! (k-1)
%o A240694 a240694_row n = a240694_tabf !! (n-1)
%o A240694 a240694_tabf = map (scanl1 (*)) a027750_tabf
%o A240694 (PARI) row(n) = my(d=divisors(n)); vector(#d, k, prod(i=1, k, d[i])); \\ _Michel Marcus_, Jan 24 2022
%Y A240694 Cf. A000005 (row lengths), A007955, A020639, A027750, A240698.
%K A240694 nonn,tabf
%O A240694 1,3
%A A240694 _Reinhard Zumkeller_, Apr 10 2014