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a(1) = 1, a(n) = a(n-1) + phi(a(n-1)).
3

%I #23 Oct 07 2020 09:23:29

%S 1,2,3,5,9,15,23,45,69,113,225,345,521,1041,1733,3465,4905,7497,11529,

%T 18009,29097,47817,71577,114777,184761,307881,482841,804573,1212813,

%U 1854333,2993517,4953069,7752429,12826269,21376953,34207353,55027593,91712493,152705493

%N a(1) = 1, a(n) = a(n-1) + phi(a(n-1)).

%C Partial sums of A165931. - _Jaroslav Krizek_, Sep 30 2009

%H Alois P. Heinz, <a href="/A074693/b074693.txt">Table of n, a(n) for n = 1..500</a> (first 300 terms from T. D. Noe)

%F 1 < a(n+1)/a(n) <= 2 . Does limit a(n+1)/a(n) exist ?

%p a:= proc(n) option remember; `if`(n=1, 1,

%p numtheory[phi](a(n-1))+a(n-1))

%p end:

%p seq(a(n), n=1..50); # _Alois P. Heinz_, Oct 02 2020

%t NestList[# + EulerPhi@ # &, 1, 36] (* _Robert G. Wilson v_, Mar 02 2011 *)

%Y Cf. A000010, A165931.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Sep 03 2002