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A244965 Triangle read by rows: T(n,k) = sum of the k-th divisor island of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

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 A143908 A117572

Adjacent sequences:  A244962 A244963 A244964 * A244966 A244967 A244968

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jul 24 2014

STATUS

approved

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Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)