A228813 Triangle read by rows T(n,k) in which column k lists 1's interleaved with A004526(k-1) zeros starting from the row A002620(k+1), with n>=1, k>=1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0

Offset

1

Comments

The sum of row n equals the number of divisors of n.

The number of zeros in row n equals A078152(n).

It appears that there are only eight rows that do not contain zeros. The indices of these rows are 1, 2, 3, 4, 6, 8, 12, 24, the divisors of 24, see A018253.

It appears that A066522 gives the indices of the rows in which the elements are in nonincreasing order.

Links

Table of n, a(n) for n=1..90.

Example

For n = 10, row 10 is [1, 1, 1, 1, 0], and the sum of row 10 is 1+1+1+1+0 = 4. On the other hand, 10 has four divisors: 1, 2, 5, and 10. Note that the sum of row 10 is also A000005(10) = 4, the number of divisors of 10.
Triangle begins:
1;
1, 1;
1, 1;
1, 1, 1;
1, 1, 0;
1, 1, 1, 1;
1, 1, 0, 0;
1, 1, 1, 1;
1, 1, 0, 0, 1;
1, 1, 1, 1, 0;
1, 1, 0, 0, 0;
1, 1, 1, 1, 1, 1;
1, 1, 0, 0, 0, 0;
1, 1, 1, 1, 0, 0;
1, 1, 0, 0, 1, 1;
1, 1, 1, 1, 0, 0, 1;
1, 1, 0, 0, 0, 0, 0;
1, 1, 1, 1, 1, 1, 0;
1, 1, 0, 0, 0, 0, 0;
1, 1, 1, 1, 0, 0, 1, 1;
1, 1, 0, 0, 1, 1, 0, 0;
1, 1, 1, 1, 0, 0, 0, 0;
1, 1, 0, 0, 0, 0, 0, 0;
1, 1, 1, 1, 1, 1, 1, 1;
...

Crossrefs

Row sums give A000005.

Row n has length A055086(n).

Columns 1 and 2: A000012. Columns 3 and 4: A059841.

Columns 5 and 6: A079978. Columns 7 and 8: A121262.

Columns 9 and 10: A079998. Columns 11 and 12: A079979.

Columns 13 and 14: A082784.

Cf. A002620, A004526, A018253, A027750, A066522, A078152, A147861, A161904, A196020, A210959, A212119, A212120, A221645, A228812, A228814.

Sequence in context: A152066 A334946 A225595 * A122255 A122261 A015120

Adjacent sequences: A228810 A228811 A228812 * A228814 A228815 A228816

Keyword

nonn,tabf

Author

Omar E. Pol, Sep 29 2013

Status

approved