cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

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Author

Rémy Sigrist, Jan 12 2023

Keywords

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).

Examples

			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]
		

Crossrefs

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

Programs

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

Formula

T(n,1) = 1.
T(n, A307314(n)) = A359708(n).
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