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A295502 a(n) = phi(5^n-1), where phi is Euler's totient function (A000010).

%I A295502 #28 Feb 16 2025 08:33:52
%S A295502 2,8,60,192,1400,4320,39060,119808,894240,2912000,24414060,62208000,
%T A295502 610351560,1959874560,13154400000,44043337728,380537036928,
%U A295502 997843069440,9485297382000,25606963200000,230106651919200,748687423334400,5959800062798400,15138938880000000
%N A295502 a(n) = phi(5^n-1), where phi is Euler's totient function (A000010).
%C A295502 Faye et al. prove that no term is of the form 5^k-1. - _Michel Marcus_, Jun 16 2024
%H A295502 Max Alekseyev, <a href="/A295502/b295502.txt">Table of n, a(n) for n = 1..502</a>
%H A295502 Bernadette Faye, Florian Luca, and Amadou Tall, <a href="https://doi.org/10.4134/BKMS.2015.52.2.513">On the equation phi(5^m-1)=5^n-1</a>, Bull. Korean Math. Soc. 2015; 52(2): 513-524.
%H A295502 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>
%H A295502 Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler%27s_phi_function">Euler's totient function</a>
%F A295502 a(n) = n*A027741(n).
%F A295502 a(n) = A000010(A024049(n)). - _Michel Marcus_, Jun 16 2024
%t A295502 EulerPhi[5^Range[25] - 1] (* _Paolo Xausa_, Jun 18 2024 *)
%o A295502 (PARI) {a(n) = eulerphi(5^n-1)}
%Y A295502 Cf. A000010, A024049.
%Y A295502 phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), this sequence (k=5), A366623 (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).
%K A295502 nonn
%O A295502 1,1
%A A295502 _Seiichi Manyama_, Nov 22 2017