A319214 a(n) = phi(n^5 - 1)/5 where phi is A000010.

6, 22, 120, 280, 1240, 1120, 5400, 5280, 12960, 12880, 45240, 24752, 90240, 59160, 96000, 141984, 346880, 163800, 540000, 326720, 588984, 585120, 1523280, 582400, 1728000, 1203840, 2294712, 1758096, 4692408, 1388000, 6480000, 3787200, 5416800, 4783680, 7440000

Offset: 2

Author

Seiichi Manyama, Sep 13 2018

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Totient Function.
• Wikipedia, Euler's totient function.

Crossrefs

Row 5 of A369291.

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

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

Programs

Mathematica

Table[EulerPhi[n^5-1]/5,{n,2,40}] (* Harvey P. Dale, Feb 09 2019 *)

PARI

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

Formula

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