A368198 a(n) gives the number of ways to go from n to 1 with steps consisting of replacing a positive number without leading zero, say m, appearing in the decimal expansion of a number, by a proper divisor of m.

1, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 9, 2, 13, 4, 20, 2, 31, 4, 8, 4, 16, 7, 54, 10, 51, 10, 123, 16, 14, 2, 39, 7, 58, 9, 118, 5, 136, 17, 20, 6, 55, 16, 149, 25, 157, 19, 459, 44, 16, 5, 71, 8, 138, 12, 249, 13, 263, 18, 47, 8, 76, 33, 276, 35, 336, 26, 714, 87

Offset: 1

Author

Rémy Sigrist, Dec 16 2023

Keywords

• nonn
• base

Examples

			a(12) = 9 for we have nine ways to go from 12 to 1:
    12 -> 1,
    12 -> 2 -> 1,
    12 -> 3 -> 1,
    12 -> 4 -> 1,
    12 -> 4 -> 2 -> 1,
    12 -> 6 -> 1,
    12 -> 6 -> 2 -> 1,
    12 -> 6 -> 3 -> 1,
    12 -> 11 -> 1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program
• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A368194, A368195, A368315 (binary variant).

Programs

PARI

See Links section.

Formula

a(1) = 1.

a(n) = Sum_{k = A368195(n)-1} a(A368194(k)) for any n > 1.