A003971 Inverse Möbius transform of A003960.

1, 2, 3, 3, 4, 6, 5, 4, 7, 8, 7, 9, 8, 10, 12, 5, 10, 14, 11, 12, 15, 14, 13, 12, 13, 16, 15, 15, 16, 24, 17, 6, 21, 20, 20, 21, 20, 22, 24, 16, 22, 30, 23, 21, 28, 26, 25, 15, 21, 26, 30, 24, 28, 30, 28, 20, 33, 32, 31, 36, 32, 34, 35, 7, 32, 42, 35, 30, 39, 40, 37, 28, 38, 40

Offset: 1

Author

Marc LeBrun

Keywords

• nonn
• easy
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A003960.

Programs

Mathematica

f[p_, e_] := (((p + 1)/2)^(e + 1) - 1)/((p - 1)/2); f[2, e_] := e + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 06 2022 *)

Formula

Multiplicative with a(p^e) = e+1 if p = 2; (((p+1)/2)^(e+1) - 1)/((p-1)/2) if p > 2. - David W. Wilson, Sep 01 2001

Extensions

More terms from Reiner Martin, Aug 15 2001

Formula corrected by Sean A. Irvine, Sep 26 2015