A319214 - OEIS

%I #24 Dec 09 2024 05:28:44

%S 6,22,120,280,1240,1120,5400,5280,12960,12880,45240,24752,90240,59160,

%T 96000,141984,346880,163800,540000,326720,588984,585120,1523280,

%U 582400,1728000,1203840,2294712,1758096,4692408,1388000,6480000,3787200,5416800,4783680,7440000

%N a(n) = phi(n^5 - 1)/5 where phi is A000010.

%H Seiichi Manyama, <a href="/A319214/b319214.txt">Table of n, a(n) for n = 2..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's totient function</a>.

%F Sum_{k=1..n} a(k) = c * n^6 + O((n*log(n))^5), where c = (1/30) * Product_{p prime == 1 (mod 5)} (1 - 5/p^2) * Product_{p prime !== 1 (mod 5)} (1 - 1/p^2) = 0.019389107739... . - _Amiram Eldar_, Dec 09 2024

%t Table[EulerPhi[n^5-1]/5,{n,2,40}] (* _Harvey P. Dale_, Feb 09 2019 *)

%o (PARI) {a(n) = eulerphi(n^5-1)/5}

%Y Row 5 of A369291.

%Y Cf. A000010, A258807 (n^5-1).

%Y phi(n^b - 1)/b: A319210 (b=2), A319213 (b=3), this sequence (b=5).

%K nonn,easy

%O 2,1

%A _Seiichi Manyama_, Sep 13 2018