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

1,2

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.

Links

Table of n, a(n) for n=1..112.

Example

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.

Sequence in context: A316339 A186971 A329255 * A096827 A298321 A226142

Adjacent sequences: A262532 A262533 A262534 * A262536 A262537 A262538

Keyword

nonn,tabf

Author

Omar E. Pol, Sep 24 2015

Status

approved