A244965 Triangle read by rows: T(n,k) = sum of the k-th divisor island of n.

1, 3, 1, 3, 3, 4, 1, 5, 6, 6, 1, 7, 3, 4, 8, 1, 3, 9, 3, 5, 10, 1, 11, 10, 6, 12, 1, 13, 3, 7, 14, 1, 3, 5, 15, 3, 4, 8, 16, 1, 17, 6, 6, 9, 18, 1, 19, 3, 9, 10, 20, 1, 3, 7, 21, 3, 11, 22, 1, 23, 10, 6, 8, 12, 24, 1, 5, 25, 3, 13, 26, 1, 3, 9, 27, 3, 4, 7, 14, 28

Offset

1,2

Comments

A divisor island is any set of consecutive divisors of a number where no pairs of consecutive divisors in the set are separated by 2 or more.

For the number of divisor islands of n see A137921.

Row n has length A137921(n).

Row sums give A000203.

T(n,1) is a positive triangular number.

Links

Table of n, a(n) for n=1..80.

Index entries for sequences related to sigma(n)

Formula

T(n,k) = A027750(n,k), if A137921(n) = A000005(n).

Example

Written as an irregular triangle the sequence begins:
1;
3;
1, 3;
3, 4;
1, 5;
6, 6;
1, 7;
3, 4, 8;
1, 3, 9;
3, 5, 10;
1, 11;
10, 6, 12;
1, 13;
3, 7, 14;
1, 3, 5, 15;
3, 4, 8, 16;
1, 17;
6, 6, 9, 18;
1, 19;
3, 9, 10, 20;
...
For n = 20 and k = 2 the divisors of 20 are [1, 2, 4, 5, 10, 20], there are four divisor islands: [1, 2], [4, 5], [10], [20] and the sum of the second divisor island is 4 + 5 = 9, so T(20,2) = 9.

Crossrefs

Cf. A000203, A000217, A027750, A137921.

Sequence in context: A211974 A136297 A243339 * A049996 A344793 A143908

Adjacent sequences: A244962 A244963 A244964 * A244966 A244967 A244968

Keyword

nonn,tabf

Author

Omar E. Pol, Jul 24 2014

Status

approved