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%I #41 Aug 15 2020 09:42:14
%S 6,120,84,4320,30,30240,42,293760,252,3360,66,208565280,78,840,420,
%T 760320,102,18506880,114,131040,1890,1320,138,14182439040,150,1560,
%U 756,30240,174,668304000,186,1272960,924,2040,210,2068967577600,222,2280,1092,8910720,246
%N Smallest x such that sigma(x)/x = 2*sigma(n)/n where sigma(n) is the sum of divisors of n.
%C 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.
%C When n is even, there is no such obvious upper bound.
%C Conjecture: a(n) exists for all n.
%C It appears that a(n) is divisible by n.
%H Michel Marcus, <a href="/A246827/b246827.txt">Table of n, a(n) for n = 1..500</a>
%H M. Kozek, F. Luca, P. Pollack, and C. Pomerance, <a href="https://math.dartmouth.edu/~carlp/KozekLucaPollackPomeranceIJNTv4.pdf">Harmonious pairs</a>, p. 16, 20, IJNT, to appear.
%H Michel Marcus, <a href="/A246827/a246827.gp.txt">solveBA PARI script</a>
%H P. Pollack and C. Pomerance, <a href="https://math.dartmouth.edu/~carlp/reversal12.pdf">Some problems of Erdős on the sum-of-divisors function</a>, (2015), p. 17, 22.
%H P. Pollack, C. Pomerance, <a href="https://doi.org/10.1090/btran/10">Some problems of Erdős on the sum-of-divisors function</a>, For Richard Guy on his 99th birthday: May his sequence be unbounded, Trans. Amer. Math. Soc. Ser. B 3 (2016), 1-26.
%o (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]);}
%Y Cf. A000203, A000396, A000668, A017665, A017666.
%K nonn,look
%O 1,1
%A _Michel Marcus_, Sep 04 2014
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