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

Author

Rémy Sigrist, Dec 21 2023

Keywords

• nonn
• base
• tabf

Comments

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

Examples

			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;
    ...
		

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

Crossrefs

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

Programs

PARI

See Links section.

Formula

T(n, 1) = 1.

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