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A380415 a(n) = phi(1 + phi(3 + phi(5 + ... + phi(2*n-1)))), where phi is Euler's totient function (A000010).

%I A380415 #16 Jan 26 2025 02:46:34
%S A380415 1,2,6,12,18,22,42,42,72,20,48,18,12,108,20,42,20,42,20,36,42,42,36,
%T A380415 36,36,42,20,42,42,36,36,42,20,48,48,18,36,36,36,36,48,48,20,48,48,36,
%U A380415 20,48,96,20,96,36,20,20,42,36,36,20,36,36,36,20,20,36,36,20
%N A380415 a(n) = phi(1 + phi(3 + phi(5 + ... + phi(2*n-1)))), where phi is Euler's totient function (A000010).
%C A380415 Inspired by A380340, A380341 and A380342.
%C A380415 Conjecture 1: a(n) can be only 1, 2, 6, 12, 18, 20, 22, 36, 42, 48, 72, 96 or 108.
%C A380415 Conjecture 2: for n >= 320, a(n) = 20.
%H A380415 Paolo Xausa, <a href="/A380415/b380415.txt">Table of n, a(n) for n = 1..10000</a>
%t A380415 A380415[n_] := Fold[EulerPhi[#2 + #] &, 0, Range[2*n - 1, 1, -2]];
%t A380415 Array[A380415, 100]
%o A380415 (PARI) a(n) = my(x=0); forstep(k=n, 1, -1, x = eulerphi(2*k-1+x)); x; \\ _Michel Marcus_, Jan 24 2025
%o A380415 (Python)
%o A380415 from functools import reduce
%o A380415 from sympy import totient
%o A380415 def A380415(n): return totient(reduce(lambda x,y:totient(x)+y,range((n<<1)-1,0,-2))) # _Chai Wah Wu_, Jan 25 2025
%Y A380415 Cf. A000010, A005408, A380340, A380341, A380342, A380414.
%K A380415 nonn
%O A380415 1,2
%A A380415 _Paolo Xausa_, Jan 24 2025