A306412 a(n) = phi(n^8) = n^7*phi(n).

1, 128, 4374, 32768, 312500, 559872, 4941258, 8388608, 28697814, 40000000, 194871710, 143327232, 752982204, 632481024, 1366875000, 2147483648, 6565418768, 3673320192, 16089691302, 10240000000, 21613062492, 24943578880, 74906159834, 36691771392, 122070312500

Offset: 1

Author

Jianing Song, Feb 13 2019

Keywords

• nonn
• easy
• mult

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), A306411 (e=6), A239442 (e=7), this sequence (e=8), A239443 (e=9).

Programs

Mathematica

Table[n^7*EulerPhi[n], {n, 1, 25}] (* Amiram Eldar, Dec 06 2020 *)

PARI

a(n) = n^7 * eulerphi(n)

Formula

Multiplicative with a(p^e) = (p - 1)*p^(8*e-1).

Dirichlet g.f.: zeta(s - 8) / zeta(s - 7).

Sum_{k=1..n} a(k) ~ 2*n^9 / (3*Pi^2). See A239443 for a more general formula.

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^9 - p^8 - p + 1)) = 1.00807702579309679541... - Amiram Eldar, Dec 06 2020