OFFSET
1,2
FORMULA
a(n) = Sum_{d|n} psi(n/d) * d.
a(p) = 2*p + 1, where p is prime.
Multiplicative with a(p^e) = p^(e-1)*((p+1)*e + p). - Antti Karttunen, Aug 24 2021
MATHEMATICA
nmax = 57; CoefficientList[Series[Sum[DirichletConvolve[j, MoebiusMu[j]^2, j, k] x^k/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
f[p_, e_] := p^(e - 1)*((p + 1)*e + p); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 24 2021 *)
PROG
(PARI) mypsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
a(n) = sumdiv(n, d, mypsi(n/d)*d); \\ Michel Marcus, Sep 15 2019
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Sep 15 2019
STATUS
approved