A272025 Irregular triangle read by rows, n >= 1, 1 <= k <= A038548(n), in which T(n,k) is the sum of the k-th pair of conjugate divisors of n, or T(n,k) is the central divisor of n if such a pair does not exist.

1, 3, 4, 5, 2, 6, 7, 5, 8, 9, 6, 10, 3, 11, 7, 12, 13, 8, 7, 14, 15, 9, 16, 8, 17, 10, 4, 18, 19, 11, 9, 20, 21, 12, 9, 22, 10, 23, 13, 24, 25, 14, 11, 10, 26, 5, 27, 15, 28, 12, 29, 16, 11, 30, 31, 17, 13, 11, 32, 33, 18, 12, 34, 14, 35, 19, 36, 12, 37, 20, 15, 13, 6, 38, 39, 21, 40, 16, 41, 22, 14, 13, 42, 43, 23, 17, 13

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Omar E. Pol, Illustration of the divisors of the first 12 positive integers

Index entries for sequences related to sigma(n)

Example

Triangle begins:
  1;
  3;
  4;
  5, 2;
  6;
  7, 5;
  8;
  9, 6;
  10, 3;
  11, 7;
  12;
  13, 8, 7;
  ...
For n = 9 the divisors of 9 are [1, 3, 9]. There is only one pair of conjugate divisors: [1, 9], and the central divisor is 3, so the 9th row of the triangle is [10, 3].
For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12]. There are three pairs of conjugate divisors, they are [1, 12], [2, 6], [3, 4], so the 12th row of the triangle is [13, 8, 7].

Crossrefs

Row sums give A000203.

Row lengths give A038548.

Right border gives A207376.

Column 1 is A065475.

Cf. A027750, A210959, A228814.

Sequence in context: A239639 A099816 A237273 * A262411 A280488 A250072

Adjacent sequences: A272022 A272023 A272024 * A272026 A272027 A272028

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 21 2016

Status

approved