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%I #12 Dec 22 2023 11:39:51
%S 1,1,1,2,2,3,2,4,4,7,6,8,6,8,6,8,8,17,14,21,18,28,18,20,16,27,26,26,
%T 18,31,22,16,22,37,34,58,48,76,52,58,48,98,80,102,80,105,76,48,40,85,
%U 80,96,80,153,104,76,70,99,98,119,82,136,116,32,44,123,98
%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 binary expansion of a number, by a proper divisor of m.
%H Rémy Sigrist, <a href="/A368315/b368315.txt">Table of n, a(n) for n = 1..8192</a>
%H Rémy Sigrist, <a href="/A368315/a368315.gp.txt">PARI program</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(1) = 1.
%F a(n) = Sum_{k = A368314(n)-1} a(A368313(k)) for any n > 1.
%F a(2^k) = A011782(k) for any k >= 0.
%e a(10) = 7 for we have seven ways to go from 10 to 1:
%e 10 -> 1,
%e 10 -> 2 -> 1,
%e 10 -> 5 -> 1,
%e 10 -> 5 -> 3 -> 1,
%e 10 -> 6 -> 1,
%e 10 -> 6 -> 2 -> 1,
%e 10 -> 6 -> 3 -> 1.
%o (PARI) See Links section.
%Y Cf. A011782, A368198 (decimal variant), A368313, A368314.
%K nonn,base
%O 1,4
%A _Rémy Sigrist_, Dec 21 2023