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a(0) = 1, a(n) = n + phi(a(n-1)), where phi is Euler totient function.
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%I #9 May 23 2023 21:00:17

%S 1,2,3,5,8,9,12,11,18,15,18,17,28,25,34,31,46,39,42,31,50,41,62,53,76,

%T 61,86,69,72,53,82,71,102,65,82,75,76,73,110,79,118,99,102,75,84,69,

%U 90,71,118,107,156,99,112,101,154,115,144,105,106,111,132,101,162,117,136

%N a(0) = 1, a(n) = n + phi(a(n-1)), where phi is Euler totient function.

%C Conjecture: 1.25*n < a(n) < 4*n for n > 0.

%e a(5) = 9 because a(4) = 8 and 5 + phi(a(4)) = 5 + 4 = 9.

%p a:= proc(n) option remember;

%p `if`(n=0, 1, n+numtheory[phi](a(n-1)))

%p end:

%p seq(a(n), n=0..100); # _Alois P. Heinz_, May 20 2023

%t a[0]=1; a[n_]:=a[n]=n+EulerPhi[a[n-1]]; Array[a,65,0]

%Y Cf. A000010.

%K nonn

%O 0,2

%A _Giorgos Kalogeropoulos_, May 19 2023