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

Author

Rémy Sigrist, Apr 25 2021

Keywords

• nonn
• tabf
• base

Examples

			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]
		

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

Crossrefs

Cf. A343650.

Programs

PARI

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

Formula

T(n, 1) = 1.

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