A368198 - OEIS

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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.

2

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

(list; graph; refs; listen; history; text; internal format)

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