login
Numbers k such that s(k) = s(k+1) but phi(k) != phi(k+1), where s(k) = phi(k) + phi(phi(k)) + ... + 1 is the sum of iterated phi (A092693).
1

%I #15 Jul 24 2021 01:10:36

%S 45,297,356,375,1335,1935,3915,4743,5271,6015,6375,6903,20894,22311,

%T 25347,28118,31664,32384,39632,49155,50954,55935,59984,64514,70275,

%U 119324,125054,162944,209715,334304,342975,472718,767584,798567,862802,908775,1280096

%N Numbers k such that s(k) = s(k+1) but phi(k) != phi(k+1), where s(k) = phi(k) + phi(phi(k)) + ... + 1 is the sum of iterated phi (A092693).

%C The restriction phi(k) != phi(k+1) is intended to exclude all the (trivial) terms of A001274.

%H Amiram Eldar, <a href="/A291177/b291177.txt">Table of n, a(n) for n = 1..200</a>

%t s[n_]:=Plus @@ FixedPointList[EulerPhi, n] - (n + 1);seqQ[n_]:=(s[n+1]==s[n])&&(EulerPhi[n+1]!=EulerPhi[n]);Select[Range[10^5],seqQ]

%Y Cf. A001274, A092693.

%K nonn

%O 1,1

%A _Amiram Eldar_, Aug 19 2017