A294821 Irregular triangle read by rows: T(n,k) = 1 if k is the largest divisor of n <= sqrt(n), otherwise T(n,k) = 0. With n >= 1, and 1 <= k <= A000196(n).

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

Offset

1

Comments

The first element of column k is in the row k^2.

Links

Table of n, a(n) for n=1..110.

Formula

T(n, A033676(n)) = 1.

T(n,k) = 0 if k is not equal to A033676(n), n >= 1, and 1 <= k <= A000196(n).

a(n) = A057427(A294721(n)).

Example

Triangle begins:
1;
1;
1;
0, 1;
1, 0;
0, 1;
1, 0;
0, 1;
0, 0, 1;
0, 1, 0;
1, 0, 0;
0, 0, 1;
1, 0, 0;
0, 1, 0;
0, 0, 1;
0, 0, 0, 1;
1, 0, 0, 0;
0, 0, 1, 0;
1, 0, 0, 0;
0, 0, 0, 1;
0, 0, 1, 0;
0, 1, 0, 0;
1, 0, 0, 0;
0, 0, 0, 1;
0, 0, 0, 0, 1;
...

Mathematica

Table[ReplacePart[ConstantArray[0, IntegerPart@ Sqrt@ n], SelectFirst[Reverse@ Divisors@ n, # <= Sqrt@ n &] -> 1], {n, 32}] // Flatten (* Michael De Vlieger, Nov 13 2017 *)

Prog

(PARI) row(n) = {d = divisors(n); kmax = vecmax(select(x->(x^2 <= n), d)); vector(sqrtint(n), k, k==kmax); }
tabf(nn) = for (n=1, nn, print(row(n))); \\ Michel Marcus, Dec 12 2017

Crossrefs

Row n has length A000196(n).

Row sums give A000012.

Cf. A033676, A057427, A163280, A237273, A294721.

Sequences related to columns 1..12: A008578, A161344, A161345, A161424, A161835, A162527, A162527, A162528, A162529, A162530, A162531, A162532.

Sequence in context: A359578 A097806 A167374 * A132971 A085357 A011748

Adjacent sequences: A294818 A294819 A294820 * A294822 A294823 A294824

Keyword

nonn,tabf

Author

Omar E. Pol, Nov 09 2017

Status

approved