A368314 a(n) is the number of numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the binary expansion of n by one of the divisors of m.

1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 5, 6, 5, 5, 5, 7, 6, 7, 7, 8, 7, 8, 7, 8, 8, 9, 7, 10, 7, 6, 7, 7, 8, 10, 9, 9, 9, 9, 8, 12, 10, 11, 11, 11, 10, 10, 9, 12, 10, 11, 10, 13, 12, 12, 11, 11, 10, 15, 11, 13, 11, 7, 8, 11, 9, 9, 10, 13, 10, 13, 11, 12, 14, 12

Offset

1,2

Comments

a(n) gives the number of terms in the n-th row of A368313.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, PARI program

Index entries for sequences related to binary expansion of n

Formula

a(n) >= A000005(n).

a(2^k) = k + 1 for any k >= 0.

Example

For n = 42: the 42nd row of A368313 contains 12 terms (1, 2, 3, 5, 6, 7, 10, 14, 21, 22, 26, 42), so a(42) = 12.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000005, A368195 (decimal variant), A368313.

Sequence in context: A161511 A319856 A100197 * A356874 A057022 A287896

Adjacent sequences: A368311 A368312 A368313 * A368315 A368316 A368317

Keyword

nonn,base

Author

Rémy Sigrist, Dec 21 2023

Status

approved