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%I #15 Dec 22 2023 11:39:43
%S 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,
%T 14,2,39,7,58,9,118,5,136,17,20,6,55,16,149,25,157,19,459,44,16,5,71,
%U 8,138,12,249,13,263,18,47,8,76,33,276,35,336,26,714,87
%N 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.
%H Rémy Sigrist, <a href="/A368198/b368198.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A368198/a368198.gp.txt">PARI program</a>
%H <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%F a(1) = 1.
%F a(n) = Sum_{k = A368195(n)-1} a(A368194(k)) for any n > 1.
%e a(12) = 9 for we have nine ways to go from 12 to 1:
%e 12 -> 1,
%e 12 -> 2 -> 1,
%e 12 -> 3 -> 1,
%e 12 -> 4 -> 1,
%e 12 -> 4 -> 2 -> 1,
%e 12 -> 6 -> 1,
%e 12 -> 6 -> 2 -> 1,
%e 12 -> 6 -> 3 -> 1,
%e 12 -> 11 -> 1.
%o (PARI) See Links section.
%Y Cf. A368194, A368195, A368315 (binary variant).
%K nonn,base
%O 1,4
%A _Rémy Sigrist_, Dec 16 2023
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