

A262535


Triangle read by rows T(n,k) in which column k lists the partial sums of the kth 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
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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



