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

Author

Marc LeBrun

Keywords

• nonn
• easy
• mult

Examples

			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,...
		

Links

• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A003960.

Programs

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 *)

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

Formula

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

Extensions

More terms from Reiner Martin, Aug 15 2001

Further terms from David W. Wilson, Aug 29 2001