A137921 -id:A137921 - cp's OEIS frontend

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

Omar E. Pol, Jul 24 2014

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.

			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.

Index entries for sequences related to sigma(n)

Cf. A000203, A000217, A027750, A137921.

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

cp's OEIS Frontend

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

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