OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
If k is squarefree (cf. A005117) then a(k) = k^4.
a(n) = Sum_{d|n} phi(d) * sigma(d^3).
From Amiram Eldar, May 20 2024: (Start)
Multiplicative with a(p^e) = (p^(4*e+4)-1)/(p^4-1) - (p^e-1)/(p-1).
Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = zeta(4) * zeta(5) * Product_{p prime} (1 - 1/p^4 - 1/p^5 + 1/p^6) = 1.01649108704844291655... . (End)
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#] * DivisorSigma[1, #^3] &]; Array[a, 100] (* Amiram Eldar, May 20 2024 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d^3));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 19 2024
STATUS
approved