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 A073668 Decimal expansion of Sum_{k=1..inf} 1/(10^k-1). 14
 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 3, 0, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 3, 2, 2, 4, 6, 7, 4, 8, 2, 6, 4, 8, 3, 2, 2, 4, 6, 6, 4, 8, 3, 0, 5, 4, 3, 2, 4, 4, 4, 8, 3, 2, 4, 6, 4, 4, 5, 2, 2, 6, 6, 9, 2, 8, 2, 8, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Parallels A000005 up to a(46). Sum_{k>=1} x^k/(1-x^k) = sum_{k>=1} tau(k)*x^k. Choosing x = 1/10 gives the result. - Amarnath Murthy, Oct 21 2002 REFERENCES Amarnath Murthy, Some interesting results on d(N), the number of divisors of a natural number, page 463, Octogon Mathematical Magazine, Vol. 8 No. 2, October 2000. LINKS FORMULA From Eric Desbiaux, Mar 11 2009: (Start) Equals Sum_{k >= 1}, 1/((2^k*5^k)-1). Equals Sum_{k >= 1}, (1/2^k)*(1/5^k)/(1-((1/2^k)*(1/5^k))). Sum_{k >= 1},1/(5^k) = 1/4. Sum_{k >= 1},1/(2^k) = 1. Sum_{k >= 1},(1/5^k)/(1-((1/2^k)*(1/5^k))) = 0.2726344339156... Sum_{k >= 1},(1/2^k)/(1-((1/2^k)*(1/5^k))) = 1.0582125127815... Sum_{k >= 1}, 1/(1-((1/2^k)*(1/5^k))) - 1 = A073668. (End) EXAMPLE 0.122324243426244526264428344628264449244... = A065444/9. MAPLE evalf(Sum(1/(10^k - 1), k = 1..infinity), 200) # Vaclav Kotesovec, Jul 16 2019 MATHEMATICA RealDigits[ N[ Sum[1/(10^k - 1), {k, 1, Infinity}], 120]] [[1]] x = 1/10; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* Robert G. Wilson v, Oct 12 2014 after the formula of Amarnath Murthy *) PROG (PARI) suminf(k=1, 1/(10^k-1)) \\ Charles R Greathouse IV, Oct 05 2014 CROSSREFS Sequence in context: A000005 A122667 A122668 * A302051 A066800 A218705 Adjacent sequences:  A073665 A073666 A073667 * A073669 A073670 A073671 KEYWORD cons,nonn AUTHOR Robert G. Wilson v, Aug 29 2002 STATUS approved

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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)