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A212120 Triangle read by rows T(n,k), n>=1, k>=1, where T(n,k) is the sum of the divisors d of n with min(d, n/d) = k. 6
1, 3, 5, 7, 1, 9, 1, 11, 3, 13, 3, 15, 5, 17, 5, 1, 19, 7, 1, 21, 7, 1, 23, 9, 3, 25, 9, 3, 27, 11, 3, 29, 11, 5, 31, 13, 5, 1, 33, 13, 5, 1, 35, 15, 7, 1, 37, 15, 7, 1, 39, 17, 7, 3, 41, 17, 9, 3, 43, 19, 9, 3, 45, 19, 9, 3, 47, 21, 11, 5, 49, 21, 11, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column k lists the odd numbers repeated k times starting in row k^2.

1 together with the first differences of the row sums give the divisor function A000005.

T(n,k) is also the total number of divisors of all positive integers <= n on the edges of k-th triangle in the diagram of divisors (see link section). See also A212119.

LINKS

Table of n, a(n) for n=1..75.

Omar E. Pol, , Diagram of divisors, figure 1, figure 2

FORMULA

T(n,k) = Sum_{j=1..n) A212119(j,k).

EXAMPLE

Written as an irregular triangle the sequence begins:

1;

3;

5;

7,   1;

9,   1;

11,  3;

13,  3;

15,  5;

17,  5,  1;

19,  7,  1;

21,  7,  1;

23,  9,  3;

25,  9,  3;

27, 11,  3;

29, 11,  5;

31, 13,  5,  1;

33, 13,  5,  1;

35, 15,  7,  1;

37, 15,  7,  1;

39, 17,  7,  3;

41, 17,  9,  3;

43, 19,  9,  3;

45, 19,  9,  3;

47, 21, 11,  5;

49, 21, 11,  5,  1;

CROSSREFS

Row sums give A006218, n >= 1.

Columns (1-5): A005408, A109613, A130823, A129756, A130497.

Cf. A000005, A027750, A010766, A147861, A163100, A212119.

Sequence in context: A266295 A172049 A021032 * A128059 A084763 A179650

Adjacent sequences:  A212117 A212118 A212119 * A212121 A212122 A212123

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jul 02 2012

EXTENSIONS

Definition changed by Franklin T. Adams-Watters, Jul 12 2012

STATUS

approved

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Last modified June 19 04:44 EDT 2019. Contains 324217 sequences. (Running on oeis4.)