A192266 Decimal expansion of Sum_{k >= 1} 1/k^sigma_*(k) where sigma_*(n) is the sum of the anti-divisors of n.

2, 1, 2, 7, 8, 2, 7, 8, 0, 2, 4, 2, 5, 0, 7, 1, 7, 8, 3, 0, 4, 4, 1, 3, 1, 7, 4, 6, 9, 6, 6, 0, 9, 9, 2, 6, 2, 4, 5, 0, 7, 7, 3, 5, 3, 0, 8, 3, 4, 1, 9, 8, 9, 7, 3, 0, 9, 4, 3, 0, 6, 8, 3, 7, 1, 7, 1, 8, 7, 1, 8, 2, 8, 4, 3, 0, 3, 2, 7, 1, 4, 2, 5, 6, 4, 8

Offset

1,1

Comments

Continued fraction (2,7,1,4,1,1,1,6,4,1,11,1,2...).

Links

Table of n, a(n) for n=1..86.

Example

1/1^sigma*(1)+ 1/2^sigma*(2) + 1/3^sigma*(3) + 1/4^sigma*(4) + 1/5^sigma*(5) + 1/6^sigma*(6) + ... = 1/1^0 + 1/2^0 + 1/3^2 + 1/4^3 + 1/5^5 + 1/6^4 + ... = 2.12782780242507..

Maple

with(numtheory): P:=proc(i) local a, j, k, n, s; d:=2; for n from 3 to i do k:=0; j:=n;
while j mod 2 <> 1 do k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
d:=d+1/n^a; od; print(evalf(d, 300)); end: P(100);

Mathematica

f[n_] := Total@ Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; First@ RealDigits@ N[Sum[1/k^f@ k, {k, 120}], 86] (* Michael De Vlieger, Oct 08 2015 *)

Crossrefs

Cf. A066417, A192265.

Sequence in context: A021051 A113246 A358604 * A056887 A360025 A144803

Adjacent sequences: A192263 A192264 A192265 * A192267 A192268 A192269

Keyword

nonn,cons

Author

Paolo P. Lava, Jun 27 2011

Extensions

Corrected and edited by R. J. Mathar, Jun 27 2011

Status

approved