

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
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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 sumofdivisors function, (2015), p. 17, 22.
P. Pollack, C. Pomerance, Some problems of Erdos on the sumofdivisors 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



