A370296 - OEIS

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A370296

Inverse Moebius transform of A322327.

1, 3, 3, 7, 3, 9, 3, 13, 7, 9, 3, 21, 3, 9, 9, 21, 3, 21, 3, 21, 9, 9, 3, 39, 7, 9, 13, 21, 3, 27, 3, 31, 9, 9, 9, 49, 3, 9, 9, 39, 3, 27, 3, 21, 21, 9, 3, 63, 7, 21, 9, 21, 3, 39, 9, 39, 9, 9, 3, 63, 3, 9, 21, 43, 9, 27, 3, 21, 9, 27, 3, 91, 3, 9, 21, 21, 9, 27, 3, 63, 21, 9, 3, 63

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..84.

FORMULA

Multiplicative with a(p^e) = 1 + e + e^2 for prime p and e >= 0.

Dirichlet g.f.: (zeta(s))^3 * zeta(2*s) / zeta(4*s).

Dirichlet inverse sequence b(n) for n > 0 is multiplicative with b(p) = -3 and b(p^e) = 2 * (-1)^((e+1)*(e+2)/2) for prime p and e > 1.

Dirichlet convolution of A000005 and A323308.

MATHEMATICA

f[p_, e_] := e^2 + e + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 14 2024 *)