A346795 Irregular triangle T(n, k), n > 0, k = 1..A091220(n), read by rows; the n-th row gives, in ascending order, the distinct integers k such that A048720(k, m) = n for some m.

1, 1, 2, 1, 3, 1, 2, 4, 1, 3, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 7, 9, 1, 2, 3, 5, 6, 10, 1, 11, 1, 2, 3, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 4, 8, 16, 1, 3, 5, 15, 17, 1, 2, 3, 6, 7, 9, 14, 18, 1, 19, 1, 2, 3, 4, 5, 6, 10, 12, 20, 1, 7, 21

Offset

1,3

Comments

The n-th row corresponds to the divisors of the n-th GF(2)[X]-polynomial.

The greatest value both in the n-th row and in the k-th row corresponds to A091255(n, k).

The index of the first row containing both n and k corresponds to A091256(n, k).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..9228 (first 1024 rows flattened)

Rémy Sigrist, PARI program for A346795

Index entries for sequences operating on GF(2)[X]-polynomials

Formula

T(n, 1) = 1.

T(n, A091220(n)) = n.

Sum_{k = 1..A091220(n)} T(n, k) = A280493(n).

T(n, 1) XOR ... XOR T(n, A091220(n)) = A178908(n) (where XOR denotes the bitwise XOR operator).

Example

The triangle starts:
      1:   [1]
      2:   [1, 2]
      3:   [1, 3]
      4:   [1, 2, 4]
      5:   [1, 3, 5]
      6:   [1, 2, 3, 6]
      7:   [1, 7]
      8:   [1, 2, 4, 8]
      9:   [1, 3, 7, 9]
     10:   [1, 2, 3, 5, 6, 10]
     11:   [1, 11]
     12:   [1, 2, 3, 4, 6, 12]
     13:   [1, 13]
     14:   [1, 2, 7, 14]
     15:   [1, 3, 5, 15]

Prog

(PARI) See Links section.

Crossrefs

Cf. A048720, A091220, A091255, A091256, A091257, A178908, A280493, A348135.

Sequence in context: A222818 A057059 A368313 * A361172 A169896 A210208

Adjacent sequences: A346792 A346793 A346794 * A346796 A346797 A346798

Keyword

nonn,tabf

Author

Rémy Sigrist, Sep 29 2021

Status

approved