A066772 Continued fraction expansion for Sum_{k>=1} d(k)/2^k where d(k) are divisors of k, 1 <= d <= k.

2, 1, 2, 1, 9, 1, 2, 1, 1, 1, 5, 8, 1, 3, 2, 3, 2, 2, 2, 2, 1, 3, 3, 4, 12, 1, 1, 1, 11, 4, 15, 6, 3, 3, 2, 1, 20, 4, 4, 1, 4, 1, 2, 1, 2, 6, 1, 2, 1, 28, 107, 1, 4, 4, 3, 1, 2, 2, 4, 2, 3, 51, 1, 1, 1, 4, 2, 4, 1, 20, 20, 1, 14, 3, 27, 1, 4, 3, 14, 329, 1, 1, 1, 111, 2, 3, 1, 2, 1, 4, 1, 6, 1, 4, 1

Offset: 0

Author

Randall L Rathbun, Jan 16 2002

Keywords

• nonn
• cofr

Comments

A(1669) accurate to 500 decimal digits.

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.

Links

• Steven R. Finch, Digital Search Tree Constants [Broken link]
• Steven R. Finch, Digital Search Tree Constants [From the Wayback machine]

Crossrefs

Cf. A066766 (decimal expansion).

Programs

PARI

{smv(v)= s=0; for(i=1,matsize(v)[2],s=s+v[i]); s }
{A066766(n)= sm=0; for(j=1,n,sm=sm+smv(divisors(j)/2^j)); sm*1.0 }

PARI

contfrac(suminf(k=1, sigma(k)/2^k)) \\ Michel Marcus, Apr 25 2022

Extensions

Offset changed by Andrew Howroyd, Jul 04 2024