This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380342 #29 Jan 27 2025 06:22:39 %S A380342 1,4,12,12,36,40,36,72,156,112,48,112,110,116,72,72,36,88,72,88,116, %T A380342 88,88,36,48,72,88,96,88,88,88,116,116,72,36,88,116,116,36,88,116,112, %U A380342 48,72,112,116,116,116,116,116,88,88,72,88,116,116,88,72,88,88,88,36,116 %N A380342 a(n) = phi(1 + phi(8 + phi(27 + ... phi(n^3)))). %C A380342 a(n) is either 1, 4, 12, 36, 40, 48, 72, 88, 96, 110, 112, 116, or 156 (see Vela and Wolird). - _Chai Wah Wu_, Jan 22 2025 %H A380342 Chai Wah Wu, <a href="/A380342/b380342.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paolo Xausa) %H A380342 Luis Palacios Vela and Christian Wolird, <a href="https://arxiv.org/abs/2501.10616">The Forestry of Adversarial Totient Iterations</a>, arXiv:2501.10616 [math.NT], 2025. %t A380342 A380342[n_] := Fold[EulerPhi[#2 + #] &, 0, Range[n, 1, -1]^3]; %t A380342 Array[A380342, 100] (* _Paolo Xausa_, Jan 22 2025 *) %o A380342 (PARI) a(n) = my(x=0); forstep(k=n, 1, -1, x = eulerphi(x+k^3)); x; %o A380342 (Python) %o A380342 from functools import reduce %o A380342 from sympy import totient %o A380342 def A380342(n): return reduce(lambda x,y:totient(x)+y,(m**3 for m in range(n,-1,-1))) # _Chai Wah Wu_, Jan 22 2025 %Y A380342 Cf. A000010, A380340, A380341, A380354, A380414, A380415. %K A380342 nonn %O A380342 1,2 %A A380342 _Michel Marcus_, Jan 22 2025