A240698 Partial sums of divisors of n, cf. A027750.

1, 1, 3, 1, 4, 1, 3, 7, 1, 6, 1, 3, 6, 12, 1, 8, 1, 3, 7, 15, 1, 4, 13, 1, 3, 8, 18, 1, 12, 1, 3, 6, 10, 16, 28, 1, 14, 1, 3, 10, 24, 1, 4, 9, 24, 1, 3, 7, 15, 31, 1, 18, 1, 3, 6, 12, 21, 39, 1, 20, 1, 3, 7, 12, 22, 42, 1, 4, 11, 32, 1, 3, 14, 36, 1, 24, 1

Offset

1,3

Comments

Triangle read by rows in which row n lists the partial sums 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,A000005(n)) = A000203(n);

T(n,A000005(n)-1) = A001065(n), n > 1.

Example

.    n |  n-th row of A240698   |  n-th row of A027750
.  ----+------------------------+---------------------
.    1 |  1                     |  1
.    2 |  1, 3                  |  1, 2
.    3 |  1, 4                  |  1, 3
.    4 |  1, 3, 7               |  1, 2, 4
.    5 |  1, 6                  |  1, 5
.    6 |  1, 3, 6, 12           |  1, 2, 3, 6
.    7 |  1, 8                  |  1, 7
.    8 |  1, 3, 7, 15           |  1, 2, 4, 8
.    9 |  1, 4, 13              |  1, 3, 9
.   10 |  1, 3, 8, 18           |  1, 2, 5, 10
.   11 |  1, 12                 |  1, 11
.   12 |  1, 3, 6, 10, 16, 28   |  1, 2, 3, 4, 6, 12
.   13 |  1, 14                 |  1, 13 .

Mathematica

Table[Accumulate[Divisors[n]], {n, 30}]//Flatten (* Harvey P. Dale, Dec 30 2019 *)

Prog

(Haskell)
a240698 n k = a240698_tabf !! (n-1) !! (k-1)
a240698_row n = a240698_tabf !! (n-1)
a240698_tabf = map (scanl1 (+)) a027750_tabf
(PARI) row(n) = my(d=divisors(n)); vector(#d, k, sum(i=1, k, d[i])); \\ Michel Marcus, Jan 24 2022

Crossrefs

Cf. A000005 (row lengths), A240694.

Cf. A000203, A001065, A027750, A064510, A194472.

Sequence in context: A278536 A143825 A290478 * A010602 A120731 A294098

Adjacent sequences: A240695 A240696 A240697 * A240699 A240700 A240701

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Apr 10 2014

Status

approved