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A272026 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the numbers A016945 interleaved with k-1 zeros, and the first element of column k is in row k(k+1)/2. 2
3, 9, 15, 3, 21, 0, 27, 9, 33, 0, 3, 39, 15, 0, 45, 0, 0, 51, 21, 9, 57, 0, 0, 3, 63, 27, 0, 0, 69, 0, 15, 0, 75, 33, 0, 0, 81, 0, 0, 9, 87, 39, 21, 0, 3, 93, 0, 0, 0, 0, 99, 45, 0, 0, 0, 105, 0, 27, 15, 0, 111, 51, 0, 0, 0, 117, 0, 0, 0, 9, 123, 57, 33, 0, 0, 3, 129, 0, 0, 21, 0, 0, 135, 63, 0, 0, 0, 0, 141, 0, 39, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Alternating sum of row n equals 3 times sigma(n), i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = 3*A000203(n) = A272027(n).

Row n has length A003056(n) hence the first element of column k is in row A000217(k).

The number of positive terms in row n is A001227(n).

If T(n,k) = 9 then T(n+1,k+1) = 3 is the first element of the column k+1.

For more information see A196020.

LINKS

Table of n, a(n) for n=1..94.

FORMULA

T(n,k) = 3*A196020(n,k) = A196020(n,k) + A236106(n,k).

EXAMPLE

Triangle begins:

3;

9;

15,   3;

21,   0;

27,   9;

33,   0,  3;

39,  15,  0;

45,   0,  0;

51,  21,  9;

57,   0,  0,  3;

63,  27,  0,  0;

69,   0, 15,  0;

75,  33,  0,  0;

81,   0,  0,  9;

87,  39, 21,  0,  3;

93,   0,  0,  0,  0;

99,  45,  0,  0,  0;

105,  0, 27, 15,  0;

111, 51,  0,  0,  0;

117,  0,  0,  0,  9;

123, 57, 33,  0,  0,  3;

129,  0,  0, 21,  0,  0;

135, 63,  0,  0,  0,  0;

141,  0, 39,  0,  0,  0;

...

For n = 9 the divisors of 9 are 1, 3, 9, therefore the sum of the divisors of 9 is 1 + 3 + 9 = 13 and 3*13 = 39. On the other hand the 9th row of triangle is 51, 21, 9, therefore the alternating row sum is 51 - 21 + 9 = 39, equaling 3 times sigma(9).

CROSSREFS

Column 1 is A016945.

Cf. A000203, A001227, A003056, A074400, A196020, A236106, A237048, A237593, A239050, A239662, A244050, A272027.

Sequence in context: A317692 A175351 A050005 * A152247 A253765 A077932

Adjacent sequences:  A272023 A272024 A272025 * A272027 A272028 A272029

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 18 2016

STATUS

approved

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Last modified July 21 00:49 EDT 2019. Contains 325189 sequences. (Running on oeis4.)