A343651 Irregular triangle T(n, k), n > 0, k = 1..A343650(n), read by rows; the n-th row lists the divisors d of n such that the product d * (n/d) can be computed without carries in binary.

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 2, 3, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 4, 8, 16, 1, 17, 1, 2, 9, 18, 1, 19, 1, 2, 4, 5, 10, 20, 1, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 25

Offset

1,3

Links

Rémy Sigrist, Table of n, a(n) for n = 1..4788 (rows for n = 1..1024)

Index entries for sequences related to binary expansion of n

Index entries for sequences related to divisors

Formula

T(n, 1) = 1.

T(n, A343650(n)) = n.

Example

Triangle T(n, k) begins:
     1:     [1]
     2:     [1, 2]
     3:     [1, 3]
     4:     [1, 2, 4]
     5:     [1, 5]
     6:     [1, 2, 3, 6]
     7:     [1, 7]
     8:     [1, 2, 4, 8]
     9:     [1, 9]
    10:     [1, 2, 5, 10]
    11:     [1, 11]
    12:     [1, 2, 3, 4, 6, 12]
    13:     [1, 13]
    14:     [1, 2, 7, 14]
    15:     [1, 3, 5, 15]

Prog

(PARI) row(n, h=hammingweight) = my (hn=h(n)); select(d -> hn==h(d)*h(n/d), divisors(n))

Crossrefs

Cf. A343650.

Sequence in context: A027750 A275055 A254679 * A355634 A275280 A319845

Adjacent sequences: A343648 A343649 A343650 * A343652 A343653 A343654

Keyword

nonn,tabf,base

Author

Rémy Sigrist, Apr 25 2021

Status

approved