A361148 a(n) = phi(n)^4.
1, 1, 16, 16, 256, 16, 1296, 256, 1296, 256, 10000, 256, 20736, 1296, 4096, 4096, 65536, 1296, 104976, 4096, 20736, 10000, 234256, 4096, 160000, 20736, 104976, 20736, 614656, 4096, 810000, 65536, 160000, 65536, 331776, 20736, 1679616, 104976, 331776, 65536, 2560000
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Vaclav Kotesovec, Plot of c(k)*log(k), for k = 1..350
Programs
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Mathematica
Table[EulerPhi[n]^4, {n, 1, 50}] -
PARI
a(n) = eulerphi(n)^4;
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PARI
for(n=1, 100, print1(direuler(p=2, n, (1 + X - 4*p*X + 6*p^2*X - 4*p^3*X) / (1 - p^4*X))[n], ", "))
Formula
Multiplicative with a(p^e) = (p-1)^4 * p^(4*e-4).
Dirichlet g.f.: zeta(s-4) * Product_{primes p} (1 + 1/p^s - 4/p^(s-1) + 6/p^(s-2) - 4/p^(s-3)).
Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = Product_{primes p} (1 - 4/p^2 + 6/p^3 - 4/p^4 + 1/p^5) = 0.286256471511560891173288340086638647956074700525046868161...
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p^4/((p-1)^4*(p^4-1))) = 2.20815077889083518654... . - Amiram Eldar, Sep 01 2023
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