A262535 Triangle read by rows T(n,k) in which column k lists the partial sums of the k-th column of triangle A261699.

1, 2, 3, 3, 4, 3, 5, 8, 6, 8, 3, 7, 15, 3, 8, 15, 3, 9, 24, 6, 10, 24, 6, 5, 11, 35, 6, 5, 12, 35, 9, 5, 13, 48, 9, 5, 14, 48, 9, 12, 15, 63, 12, 12, 5, 16, 63, 12, 12, 5, 17, 80, 12, 12, 5, 18, 80, 15, 21, 5, 19, 99, 15, 21, 5, 20, 99, 15, 21, 10, 21, 120, 18, 21, 10, 7, 22, 120, 18, 32, 10, 7, 23, 143, 18, 32, 10, 7, 24, 143, 21, 32, 10, 7, 25, 168, 21, 32, 15, 7, 26, 168, 21, 45, 15, 7, 27, 195, 24, 45, 15, 16

Offset: 1

Author

Omar E. Pol, Sep 24 2015

Keywords

• nonn
• tabf

Comments

Conjecture: the sum of row n gives A078471(n), the sum of all odd divisors of all positive integers <= n.

Row n has length A003056(n) hence column k starts in row A000217(k).

Column 1 gives A000027.

Examples

			Triangle begins:
1;
2;
3,    3;
4,    3;
5,    8;
6,    8,  3;
7,   15,  3;
8,   15,  3;
9,   24,  6;
10,  24,  6,  5;
11,  35,  6,  5;
12,  35,  9,  5;
13,  48,  9,  5;
14,  48,  9, 12;
15,  63, 12, 12,  5;
16,  63, 12, 12,  5;
17,  80, 12, 12,  5;
18,  80, 15, 21,  5;
19,  99, 15, 21,  5;
20,  99, 15, 21, 10;
21, 120, 18, 21, 10,  7;
22, 120, 18, 32, 10,  7;
23, 143, 18, 32, 10,  7;
24, 143, 21, 32, 10,  7;
25, 168, 21, 32, 15,  7;
26, 168, 21, 45, 15,  7;
27, 195, 24, 45, 15, 16;
...
For n = 6 the sum of all odd divisors of all positive integers <= 6 is (1) + (1) + (1 + 3) + (1) + (1 + 5) + (1 + 3) = 17. On the other hand the sum of the 6th row of triangle is 6 + 8 + 3 = 17 equaling the sum of all odd divisors of all positive integers <= 6.
		

Crossrefs

Cf. A000027, A000217, A001227, A003056, A060831, A078471, A236104, A237593, A261699.