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

1,4

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

Formula

a(1) = 1.

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A002033 A074206 A173801 * A108466 A211110 A325828

Adjacent sequences: A368195 A368196 A368197 * A368199 A368200 A368201

Keyword

nonn,base

Author

Rémy Sigrist, Dec 16 2023

Status

approved