A240698 - OEIS

%I #17 Jan 24 2022 09:20:48

%S 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,

%T 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,

%U 20,1,3,7,12,22,42,1,4,11,32,1,3,14,36,1,24,1

%N Partial sums of divisors of n, cf. A027750.

%C Triangle read by rows in which row n lists the partial sums of divisors of n. - _Omar E. Pol_, Apr 12 2014

%H Reinhard Zumkeller, <a href="/A240698/b240698.txt">Rows n = 1..1000 of table, flattened</a>

%F T(n,1) = 1, T(n,k) = T(n,k-1) + A027750(n,k), 1 < k <= n.

%F T(n,1) = 1;

%F T(n,A000005(n)) = A000203(n);

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

%e .    n |  n-th row of A240698   |  n-th row of A027750

%e .  ----+------------------------+---------------------

%e .    1 |  1                     |  1

%e .    2 |  1, 3                  |  1, 2

%e .    3 |  1, 4                  |  1, 3

%e .    4 |  1, 3, 7               |  1, 2, 4

%e .    5 |  1, 6                  |  1, 5

%e .    6 |  1, 3, 6, 12           |  1, 2, 3, 6

%e .    7 |  1, 8                  |  1, 7

%e .    8 |  1, 3, 7, 15           |  1, 2, 4, 8

%e .    9 |  1, 4, 13              |  1, 3, 9

%e .   10 |  1, 3, 8, 18           |  1, 2, 5, 10

%e .   11 |  1, 12                 |  1, 11

%e .   12 |  1, 3, 6, 10, 16, 28   |  1, 2, 3, 4, 6, 12

%e .   13 |  1, 14                 |  1, 13 .

%t Table[Accumulate[Divisors[n]],{n,30}]//Flatten (* _Harvey P. Dale_, Dec 30 2019 *)

%o (Haskell)

%o a240698 n k = a240698_tabf !! (n-1) !! (k-1)

%o a240698_row n = a240698_tabf !! (n-1)

%o a240698_tabf = map (scanl1 (+)) a027750_tabf

%o (PARI) row(n) = my(d=divisors(n)); vector(#d, k, sum(i=1, k, d[i])); \\ _Michel Marcus_, Jan 24 2022

%Y Cf. A000005 (row lengths), A240694.

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

%K nonn,tabf

%O 1,3

%A _Reinhard Zumkeller_, Apr 10 2014