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URL: https://oeis.org/A359627

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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.
1
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).
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
KEYWORD
nonn,base,tabf
AUTHOR
Rémy Sigrist, Jan 12 2023
STATUS
approved