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 A332786 a(n) = numerator(-1/n + Sum_{k=1..n} 2^(k-1)/k). 1
 0, 3, 3, 61, 25, 137, 343, 32663, 2357, 74689, 66671, 5299069, 2416531, 115545821, 106974277, 637525199, 74575583, 1588674349, 4496071973, 3234136824109, 1535024393629, 5843920343363, 5575228585159, 1961561381531581, 93953561866435, 9016382638527647, 2888981280567587, 200248741591132607, 96525489421136333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If p > 3 is a prime, then p^2 | a(p). Does the above statement follow from Wolstenholme's theorem? If p is a Wolstenholme prime (A088164), then p^3 | a(p). However, it should be noted that also 7^3 | a(7). Conjecture: there are no pseudoprimes m such that m^2 | a(m). Is 7^2 the only weak pseudoprime (i.e., a composite m such that m | a(m))? LINKS FORMULA a(n) = numerator(-2/n + S(n))/2 for odd n and a(n) = numerator(-2/n + S(n)) for even n, where S(n) = Sum_{k=1..n} 2^k/k, see A108866 / A229726. a(n) = numerator(Sum_{k=1..n} (2^(k-1)-1)/k + Sum_{k=1..n-1} 1/k), see A330718 / A330719 and A001008 / A002805. EXAMPLE a(5) = numerator(-1/5 + 1/1+2/2+4/3+8/4+16/5) = numerator(128/15 - 1/5) = numerator(25/3) = 25. MATHEMATICA n = 30; Numerator[Accumulate @ Table[(2^(k-1))/k, {k, 1, n}] - 1/Range[n]] (* Amiram Eldar, Feb 24 2020 *) PROG (PARI) a(n) = numerator(-1/n + sum(k=1, n, 2^(k-1)/k)); \\ Michel Marcus, Feb 24 2020 CROSSREFS Cf. A001008, A088164, A108866, A330718. Sequence in context: A066807 A165497 A051752 * A102065 A102074 A126227 Adjacent sequences:  A332783 A332784 A332785 * A332787 A332788 A332789 KEYWORD nonn,frac AUTHOR Thomas Ordowski, Feb 24 2020 EXTENSIONS More terms from Amiram Eldar, Feb 24 2020 STATUS approved

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)