A027414 G.f. for Moebius transform is x * (1 + x) / (1 + x^4).

1, 2, 1, 2, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 0, 2, 2, 3, 1, 2, 0, 1, 1, 1, 1, 2, 2, 1, 0, 0, 1, 2, 2, 4, 0, 3, 0, 1, 0, 2, 2, 0, 1, 1, 0, 1, 1, 1, 2, 4, 2, 2, 0, 2, 0, 1, 2, 2, 1, 0, 0, 1, 1, 2, 0, 2, 1, 4, 0, 0, 1, 3, 2, 2, 1, 1, 0, 0, 1, 2, 3, 4, 1, 0, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 0, 1, 2, 3, 3, 4, 0, 2, 1, 2, 0

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			x + 2*x^2 + x^3 + 2*x^4 + x^6 + x^7 + 2*x^8 + 2*x^9 + 2*x^10 + x^11 + x^12 + ...
		

Links

• N. J. A. Sloane, Transforms

Programs

Mathematica

a[ n_] := If[ n < 1, 0, Sum[ {1, 1, 0, 0, -1, -1, 0, 0} [[ Mod[d, 8, 1]]], {d, Divisors @ n}]] (* Michael Somos, Nov 16 2011 *)

PARI

{a(n) = if( n<1, 0, sumdiv( n, d, kronecker( -4, (d-1)%8\2 + 1)))} /* Michael Somos, Sep 20 2005 */

Formula

Moebius transform is period 8 sequence [1, 1, 0, 0, -1, -1, 0, 0, ...]. - Michael Somos, Sep 20 2005

G.f.: Sum_{k>0} x^k * (1 + x^k) / (1 + x^(4*k)). - Michael Somos, Sep 20 2005

a(8*n + 5) = 0. a(8*n + 3) = A033761(n). - Michael Somos, Nov 16 2011