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

2, 8, 60, 192, 1400, 4320, 39060, 119808, 894240, 2912000, 24414060, 62208000, 610351560, 1959874560, 13154400000, 44043337728, 380537036928, 997843069440, 9485297382000, 25606963200000, 230106651919200, 748687423334400, 5959800062798400, 15138938880000000

Offset: 1

Author

Seiichi Manyama, Nov 22 2017

Keywords

• nonn

Comments

Faye et al. prove that no term is of the form 5^k-1. - Michel Marcus, Jun 16 2024

Links

• Max Alekseyev, Table of n, a(n) for n = 1..502
• Bernadette Faye, Florian Luca, and Amadou Tall, On the equation phi(5^m-1)=5^n-1, Bull. Korean Math. Soc. 2015; 52(2): 513-524.
• Eric Weisstein's World of Mathematics, Totient Function
• Wikipedia, Euler's totient function

Crossrefs

Cf. A000010, A024049.

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).

Programs

Mathematica

EulerPhi[5^Range[25] - 1] (* Paolo Xausa, Jun 18 2024 *)

PARI

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

Formula

a(n) = n*A027741(n).

a(n) = A000010(A024049(n)). - Michel Marcus, Jun 16 2024