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a(0)=1. a(n) = phi(n+a(n-1)), for n>=1, where phi(m) is the number of positive integers which are <= m and are coprime to m.
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%I #12 Apr 23 2022 14:11:21

%S 1,1,2,4,4,6,4,10,6,8,6,16,12,20,16,30,22,24,12,30,20,40,30,52,36,60,

%T 42,44,24,52,40,70,32,48,40,40,36,72,40,78,58,60,32,40,24,44,24,70,58,

%U 106,48,60,48,100,60,88,48,48,52,72,40,100,54,72,64,84,40,106,56,100

%N a(0)=1. a(n) = phi(n+a(n-1)), for n>=1, where phi(m) is the number of positive integers which are <= m and are coprime to m.

%H Harvey P. Dale, <a href="/A132857/b132857.txt">Table of n, a(n) for n = 0..1000</a>

%e a(8) + 9 = 6 + 9 = 15. There are 8 positive integers that are <= 15 and are relatively prime to 15. So a(9) = 8.

%t a = {1}; For[n = 1, n < 90, n++, AppendTo[a, EulerPhi[n + a[[ -1]]]]]; a (* _Stefan Steinerberger_, Nov 24 2007 *)

%t nxt[{n_,a_}]:={n+1,EulerPhi[n+1+a]}; NestList[nxt,{0,1},70][[All,2]] (* _Harvey P. Dale_, Apr 23 2022 *)

%K nonn

%O 0,3

%A _Leroy Quet_, Nov 21 2007

%E More terms from _Stefan Steinerberger_, Nov 24 2007