

A244965


Triangle read by rows: T(n,k) = sum of the kth 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
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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



