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A248724
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Decimal expansion of Sum_{k>=1} 1/(7^k - 1).
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10
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1, 9, 0, 9, 1, 0, 0, 6, 2, 4, 1, 0, 2, 6, 1, 5, 7, 8, 2, 0, 2, 1, 9, 9, 6, 4, 4, 4, 1, 7, 6, 9, 1, 1, 6, 8, 7, 6, 9, 2, 6, 8, 4, 7, 6, 0, 0, 8, 2, 6, 6, 4, 0, 8, 3, 3, 4, 7, 7, 1, 1, 0, 8, 6, 4, 0, 9, 9, 9, 6, 7, 5, 5, 8, 4, 6, 3, 0, 1, 4, 4, 0, 3, 8, 0, 0, 9, 1, 1, 6, 1, 6, 5, 9, 7, 0, 9, 1, 1, 9, 3, 4, 5, 6, 1
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OFFSET
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0,2
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LINKS
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FORMULA
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Equals Sum_{k>=1} d(k)/7^k, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, Jun 22 2020
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EXAMPLE
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0.1909100624102615782021996444176911687692684760082664083347711086409996755846...
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MAPLE
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# second program with faster converging series
evalf( add( (1/7)^(n^2)*(1 + 2/(7^n - 1)), n = 1..11), 105); # Peter Bala, Jan 30 2022
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MATHEMATICA
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x = 1/7; RealDigits[ Sum[ DivisorSigma[0, k] x^k, {k, 1000}], 10, 105][[1]] (* after an observation and the formula of Amarnath Murthy, see A073668 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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