A306411 a(n) = phi(n^6) = n^5*phi(n).

1, 32, 486, 2048, 12500, 15552, 100842, 131072, 354294, 400000, 1610510, 995328, 4455516, 3226944, 6075000, 8388608, 22717712, 11337408, 44569782, 25600000, 49009212, 51536320, 141599546, 63700992, 195312500, 142576512, 258280326, 206524416, 574312172, 194400000, 858874530, 536870912, 782707860, 726966784

Offset: 1

Author

Jianing Song, Feb 13 2019

Keywords

• nonn
• easy
• mult

Comments

The number of elements of the wreath product of C_n and S_6 with cycle partition equal to (6*n) is equal to 5!*a(n), where C_n is the cyclic group of order n, S_6 the symmetric group on 6 elements. - Josaphat Baolahy, Mar 13 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Eulerphi(n^e): A000010 (e=1), A002618 (e=2), A053191 (e=3), A189393 (e=4), A238533 (e=5), this sequence (e=6), A239442 (e=7), A306412 (e=8), A239443 (e=9).

Programs

Mathematica

Array[EulerPhi[#] #^5 &, 34] (* Michael De Vlieger, Feb 17 2019 *)

PARI

a(n) = n^5 * eulerphi(n)

Formula

Multiplicative with a(p^e) = (p - 1)*p^(6*e-1).

Dirichlet g.f.: zeta(s - 6) / zeta(s - 5).

Sum_{k=1..n} a(k) ~ 6*n^7 / (7*Pi^2). See A239443 for a more general formula.

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p/(p^7 - p^6 - p + 1)) = 1.03396580456393429553879930771676667947490034699829164744357501993310897305... - Vaclav Kotesovec, Sep 20 2020