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 A246827 Smallest x such that sigma(x)/x = 2*sigma(n)/n where sigma(n) is the sum of divisors of n. 1
 6, 120, 84, 4320, 30, 30240, 42, 293760, 252, 3360, 66, 208565280, 78, 840, 420, 760320, 102, 18506880, 114, 131040, 1890, 1320, 138, 14182439040, 150, 1560, 756, 30240, 174, 668304000, 186, 1272960, 924, 2040, 210, 2068967577600, 222, 2280, 1092, 8910720, 246 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS When n is odd, and if there are infinitely many Mersenne primes, then a(n) would be at most equal to n multiplied by the smallest perfect number (A000396) whose prime Mersenne component (A000668) is coprime to n. When n is even, there is no such obvious upper bound. Conjecture: a(n) exists for all n. It appears that a(n) is divisible by n. LINKS Michel Marcus, Table of n, a(n) for n = 1..500 M. Kozek, F. Luca, P. Pollack, and C. Pomerance, Harmonious pairs, p. 16, 20, IJNT, to appear. Michel Marcus, solveBA PARI script P. Pollack and C. Pomerance, Some problems of ErdÅ‘s on the sum-of-divisors function, (2015), p. 17, 22. P. Pollack, C. Pomerance, Some problems of Erdos on the sum-of-divisors function, For Richard Guy on his 99th birthday: May his sequence be unbounded, 2015, to appear. PROG (PARI) a(n) =  {nv = 2*sigma(n)/n; lim = 1; sv = []; while (#sv == 0, lim *= 10^10; sv = vecsort(solveBA(numerator(nv), denominator(nv), lim))); return (sv[1]); } CROSSREFS Cf. A000203, A000396, A000668, A017665, A017666. Sequence in context: A054957 A271648 A290341 * A127726 A117063 A178911 Adjacent sequences:  A246824 A246825 A246826 * A246828 A246829 A246830 KEYWORD nonn AUTHOR Michel Marcus, Sep 04 2014 STATUS approved

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)