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 A330245 Numbers m with a unique subset of the divisors of m that sums to m (A064771) such that sigma(m)/m > sigma(k)/k for all smaller terms k < m of A064771, where sigma(m) is the sum of divisors of m (A000203). 0
 6, 20, 78, 1014, 3774, 9514254 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Paul Erdős asked whether there are extra-weird numbers n, i.e., numbers n for which sigma(n)/n > 3, but n is not the sum of a subset of its divisors in two ways. Such numbers, if they exist, are in the intersection of A064771 and A068403, and the least of them is a term of this sequence. a(6) > 2*10^5. 10^11 < a(7) <= 105590246974194. - Giovanni Resta, Jan 14 2020 REFERENCES Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B2, p. 77. LINKS EXAMPLE The abundancy indices of the terms are sigma(a(n))/a(n) = 2 < 2.1 < 2.153... < 2.165... < 2.174... < 2.1757... MATHEMATICA okQ[n_] := Module[{d = Most[Divisors[n]]}, SeriesCoefficient[Series[ Product[ 1+x^i, {i, d}], {x, 0, n}], n] == 1]; seq = {}; rm = 0; Do[If[(r = DivisorSigma[1, n]/n) > rm && okQ[n], rm = r; AppendTo[seq, n]], {n, 1, 4000}]; seq (* after Harvey P. Dale at A064771 *) CROSSREFS Cf. A000203, A064771, A068403. Sequence in context: A240043 A058494 A147979 * A118265 A204271 A255469 Adjacent sequences:  A330242 A330243 A330244 * A330246 A330247 A330248 KEYWORD nonn,more AUTHOR Amiram Eldar, Dec 06 2019 EXTENSIONS a(6) from Giovanni Resta, Jan 14 2020 STATUS approved

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Last modified August 19 22:59 EDT 2022. Contains 356231 sequences. (Running on oeis4.)