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a(1) = 1, a(m+1) = Sum_{k=1..m} gcd(m, a(k)).
4

%I #14 Oct 18 2019 04:00:23

%S 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 61,39,117,47,29,89,31,33,161,51,75,105,37,57,159,65,41,135,43,85,251,

%U 91,139,89,127,127,171,113,157,199,131,93,227,87,117,185,121,123,227,65

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

%C From _Ivan Neretin_, Apr 06 2016: (Start)

%C a(n) >= n-1.

%C All terms except a(3) = 2 are odd.

%C For all n of the form 2^k+1 except 3, a(n) = n.

%C (End)

%H Ivan Neretin, <a href="/A056144/b056144.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t Fold[Append[#1, Total@GCD[#1, #2]] &, {1}, Range@64] (* _Ivan Neretin_, Apr 06 2016 *)

%Y Cf. A093820.

%K easy,nonn

%O 1,3

%A _Leroy Quet_, Aug 04 2000