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

Author

Rémy Sigrist, Dec 21 2023

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

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

Crossrefs

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

Programs

PARI

See Links section.

Formula

a(n) >= A000005(n).

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