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 A331343 a(n) = lcm(1,2,...,n) * Sum_{k=1..n} (2^(k-1) - 1) / k. 0
 0, 1, 9, 39, 375, 685, 8575, 30485, 162855, 291627, 5785857, 10514427, 250200951, 461037291, 854622483, 3185234481, 101381371377, 190598779657, 6833215763803, 12935721409039, 24559552771039, 46750514134519, 2051664357879617, 3923102768811707, 37581323659852375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS By Wolstenholme's theorem, if p > 3 is a prime, then p^3 | a(p). Conjecture: for n > 3, if n^3 | a(n), then n is prime. If so, there are no such pseudoprimes. Problem: are there weak pseudoprimes m such that m^2 | a(m)? None up to 5*10^4. Composite numbers m such that m | a(m) are 9, 25, 49, 99, 121, 125, 169, 221, 289, 343, 357, 361, 399, 529, 665, 841, 961, 1331, 1369, 1443, 1681, 1849, 2183, ...  Cf. A082180. Prime numbers p such that p^4 | a(p) are probably only the Wolstenholme primes A088164. LINKS Wikipedia, Wolstenholme's theorem. FORMULA a(n) = A003418(n) * A330718(n) / A330719(n). MATHEMATICA a[n_] := LCM @@ Range[n] * Sum[(2^(k-1) - 1) / k, {k, 1, n}]; Array[a, 25] PROG (MAGMA) [Lcm([1..n])*&+[(2^(k-1)-1)/k:k in [1..n]]:n in [1..25]]; // Marius A. Burtea, Jan 14 2020 (PARI) a(n) = lcm([1..n])*sum(k=1, n, (2^(k-1) - 1) / k); \\ Michel Marcus, Jan 14 2020 CROSSREFS Cf. A003418, A025529, A082180, A088164, A330718, A330719. Sequence in context: A075210 A146187 A173764 * A002085 A076603 A346336 Adjacent sequences:  A331340 A331341 A331342 * A331344 A331345 A331346 KEYWORD nonn AUTHOR Amiram Eldar and Thomas Ordowski, Jan 14 2020 STATUS approved

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Last modified May 22 17:42 EDT 2022. Contains 353957 sequences. (Running on oeis4.)