A359627 Irregular table read by rows; the n-th row lists the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.

1, 1, 2, 1, 1, 2, 4, 1, 5, 1, 2, 3, 1, 1, 2, 4, 8, 1, 9, 1, 2, 10, 1, 1, 2, 3, 4, 6, 1, 1, 2, 1, 1, 2, 4, 8, 16, 1, 17, 1, 2, 3, 9, 18, 1, 1, 2, 4, 5, 20, 1, 21, 1, 2, 1, 1, 2, 3, 4, 6, 8, 12, 1, 5, 1, 2, 1, 9, 1, 2, 4, 7, 1, 1, 2, 3, 1, 1, 2, 4, 8, 16, 32

Offset

1,3

Comments

Odd numbers share a 1-bit (2^0) with all their divisors, hence this sequence deals with even numbers.

The n-th row has A307314(n) terms, and sums to A359079(n).

Links

Table of n, a(n) for n=1..83.

Index entries for sequences related to divisors

Formula

T(n,1) = 1.

T(n, A307314(n)) = A359708(n).

Example

Table T(n, k) begins:
    [1]
    [1, 2]
    [1]
    [1, 2, 4]
    [1, 5]
    [1, 2, 3]
    [1]
    [1, 2, 4, 8]
    [1, 9]
    [1, 2, 10]
    [1]
    [1, 2, 3, 4, 6]
    [1]
    [1, 2]
    [1]
    [1, 2, 4, 8, 16]
    [1, 17]

Prog

(PARI) row(n) = { select(d -> bitand(d, 2*n)==0, divisors(2*n)) }

Crossrefs

Cf. A307314 (row lengths), A359079 (row sums), A359708.

Sequence in context: A103648 A293176 A297170 * A127309 A097853 A160266

Adjacent sequences: A359624 A359625 A359626 * A359628 A359629 A359630

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Jan 12 2023

Status

approved