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 Erdős on the sum-of-divisors function, (2015), p. 17, 22.
P. Pollack, C. Pomerance, Some problems of Erdős on the sum-of-divisors function, For Richard Guy on his 99th birthday: May his sequence be unbounded, Trans. Amer. Math. Soc. Ser. B 3 (2016), 1-26.
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
KEYWORD
nonn,look
AUTHOR
Michel Marcus, Sep 04 2014
STATUS
approved