A003970 Möbius transform of A003960 (with alternating zeros omitted).

1, 1, 2, 3, 2, 5, 6, 2, 8, 9, 3, 11, 6, 4, 14, 15, 5, 6, 18, 6, 20, 21, 4, 23, 12, 8, 26, 10, 9, 29, 30, 6, 12, 33, 11, 35, 36, 6, 15, 39, 8, 41, 16, 14, 44, 18, 15, 18, 48, 10, 50, 51, 6, 53, 54, 18, 56, 22, 12, 24, 30, 20, 18, 63, 21, 65, 27, 8, 68, 69, 23, 30, 28, 12, 74, 75

Offset

1,3

Links

Table of n, a(n) for n=1..76.

N. J. A. Sloane, Transforms.

Formula

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

Example

The Möbius transform begins 1,0,1,0,2,0,3,0,2,0,5,0,6,0,2,0,8,0,9,0,3,0,11,0,...

Mathematica

f[p_, e_] := ((p - 1)/2) ((p + 1)/2)^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[2*n - 1]; Array[a, 100] (* Amiram Eldar, Nov 03 2023 *)

Prog

(PARI) a(n) = {my(f = factor(2*n-1)); for (i=1, #f~, p = f[i, 1]; f[i, 1] = (p-1)/2*((p+1)/2)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); } \\ Michel Marcus, Feb 27 2015

Crossrefs

Cf. A003960.

Sequence in context: A113649 A307864 A066119 * A094443 A348066 A227071

Adjacent sequences: A003967 A003968 A003969 * A003971 A003972 A003973

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

More terms from Reiner Martin, Aug 15 2001

Further terms from David W. Wilson, Aug 29 2001

Status

approved