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 A192266 Decimal expansion of Sum_{k >= 1} 1/k^sigma_*(k) where sigma_*(n) is the sum of the anti-divisors of n. 2
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Continued fraction (2,7,1,4,1,1,1,6,4,1,11,1,2...). LINKS 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: A241738 A021051 A113246 * A056887 A144803 A095062 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

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)