A368313 Irregular table T(n, k), n > 0, k = 1..A368314(n), read by rows: the n-th row lists the numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the binary expansion of n by one of the divisors of m.

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

Offset

1,3

Comments

The n-th row starts with 1, ends with n, and contains the divisors of n (A027750).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10177 (rows for n = 1..2^9 flattened)

Rémy Sigrist, PARI program

Index entries for sequences related to binary expansion of n

Formula

T(n, 1) = 1.

T(n, A368314(n)) = n.

Example

Table T(n, k) begins:
    1;
    1, 2;
    1, 3;
    1, 2, 4;
    1, 3, 5;
    1, 2, 3, 6;
    1, 3, 7;
    1, 2, 4, 8;
    1, 3, 5, 9;
    1, 2, 5, 6, 10;
    1, 3, 5, 7, 11;
    1, 2, 3, 4, 6, 12;
    1, 3, 5, 7, 13;
    1, 2, 3, 6, 7, 14;
    1, 3, 5, 7, 15;
    1, 2, 4, 8, 16;
    1, 3, 5, 9, 17;
    ...

Prog

(PARI) See Links section.

Crossrefs

Cf. A027750, A368194 (decimal variant), A368314.

Sequence in context: A165416 A222818 A057059 * A346795 A361172 A169896

Adjacent sequences: A368310 A368311 A368312 * A368314 A368315 A368316

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Dec 21 2023

Status

approved