A003979 Inverse Möbius transform of A003964.

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 16, 24, 24, 31, 23, 39, 31, 42, 32, 36, 43, 60, 31, 48, 40, 56, 57, 72, 78, 63, 48, 69, 48, 91, 102, 93, 64, 90, 136, 96, 177, 84, 78, 129, 232, 124, 57, 93, 92, 112, 298, 120, 72, 120, 124, 171, 386, 168, 491, 234, 104, 127

Offset: 1

Author

Marc LeBrun

Keywords

• nonn
• easy
• mult

Links

• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A000041, A000720, A003964, A003978.

Programs

Mathematica

f[p_, e_] := Module[{q = PartitionsP[PrimePi[p] + 1]}, (q^(e+1)-1)/(q-1)]; a[n_] := Times @@ f @@@ FactorInteger[n]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Sep 04 2023 *)

Formula

Multiplicative with a(p^e) = (q^(e+1)-1)/(q-1) where q = partition(pi(p)+1) = A000041(A000720(p)+1). - David W. Wilson, Sep 01 2001

Extensions

More terms from Vladeta Jovovic, Dec 01 2001