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A322887
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Decimal expansion of the asymptotic mean value of the exponential abundancy index A051377(k)/k.
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4
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1, 1, 3, 6, 5, 7, 0, 9, 8, 7, 4, 9, 3, 6, 1, 3, 9, 0, 8, 6, 5, 2, 0, 7, 3, 1, 5, 2, 3, 8, 3, 8, 3, 2, 5, 9, 3, 4, 4, 8, 8, 0, 9, 0, 1, 8, 6, 3, 9, 5, 7, 2, 7, 6, 7, 8, 9, 0, 5, 2, 6, 5, 4, 4, 3, 1, 6, 2, 3, 9, 7, 2, 0, 3, 1, 5, 1, 5, 2, 8, 8, 3, 6, 8, 7, 6, 1, 3, 9, 2, 7, 2, 7, 4, 8, 9, 8, 5, 5, 2, 6, 2, 1, 9, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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Equals lim_{n->oo} (1/n) * Sum_{k=1..n} esigma(k)/k, where esigma(k) is the sum of exponential divisors of k (A051377).
Equals Product_{p prime} (1 + (1 - 1/p) * Sum_{k>=1} 1/(p^(3*k)-p^k)).
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EXAMPLE
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1.13657098749361390865207315238383259344880901863957...
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PROG
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(PARI) default(realprecision, 120); default(parisize, 2000000000);
my(kmax = 135); prodeulerrat(1 + (1 - 1/p) * sum(k = 1, kmax, 1/(p^(3*k)-p^k))) \\ Amiram Eldar, Mar 09 2024 (The calculation takes a few minutes.)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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