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A056144 a(1) = 1, a(m+1) = Sum_{k=1..m} gcd(m, a(k)).

%I A056144 #16 Mar 06 2025 20:19:58
%S A056144 1,1,2,3,5,9,11,7,9,27,15,21,25,13,27,49,17,33,59,19,33,69,53,45,47,
%T A056144 61,39,117,47,29,89,31,33,161,51,75,105,37,57,159,65,41,135,43,85,251,
%U A056144 91,139,89,127,127,171,113,157,199,131,93,227,87,117,185,121,123,227,65
%N A056144 a(1) = 1, a(m+1) = Sum_{k=1..m} gcd(m, a(k)).
%C A056144 From _Ivan Neretin_, Apr 06 2016: (Start)
%C A056144 a(n) >= n-1.
%C A056144 All terms except a(3) = 2 are odd.
%C A056144 For all n of the form 2^k+1 except 3, a(n) = n.
%C A056144 (End)
%H A056144 Ivan Neretin, <a href="/A056144/b056144.txt">Table of n, a(n) for n = 1..10000</a>
%e A056144 a(7) = gcd(6,1) + gcd(6,1) + gcd(6,2) + gcd(6,3) + gcd(6,5) + gcd(6,9) = 1 + 1 + 2 + 3 + 1 + 3 = 11.
%p A056144 a:= proc(n) option remember;
%p A056144       1+add(igcd(n-1, a(j)), j=2..n-1)
%p A056144     end:
%p A056144 seq(a(n), n=1..65);  # _Alois P. Heinz_, Mar 06 2025
%t A056144 Fold[Append[#1, Total@GCD[#1, #2]] &, {1}, Range@64] (* _Ivan Neretin_, Apr 06 2016 *)
%Y A056144 Cf. A093820.
%K A056144 easy,nonn
%O A056144 1,3
%A A056144 _Leroy Quet_, Aug 04 2000