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A262535 Triangle read by rows T(n,k) in which column k lists the partial sums of the k-th column of triangle A261699. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)