OFFSET
1,2
COMMENTS
If an integer m is equal to p+1 with p prime, then sigma(p)=m, and it is the maximum such number. The first numbers in the sequence 12, 42, 60, 168, 360, 744, 1512, 2418, 2880 as well as 2437344 are in this case. Curiously, at least up the last known term, this is not the case for the majority of terms of the sequence.
EXAMPLE
Only sigma(1)=1, hence the quotient is 1.
The next m is 12 with sigma(6)=sigma(11)=12, quotient 11/6 greater than 1.
Next m is 42 with [20, 26, 41] with quotient 41/20 that is greater than 11/6.
PROG
(PARI) lista(lim) = {v = vector(lim, i, sigma(i)); w = vector(lim); for (i=1, lim, vi = v[i]; if (vi <= lim, if (w[vi] == 0, w[vi] = i, w[vi] = concat(w[vi], i)); ); ); rmax = -1; for (i=1, lim, if (w[i], r = vecmax(w[i]) / vecmin(w[i]); if (r > rmax, print1(i, ", "); rmax = r; ); ); ); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 30 2014
EXTENSIONS
a(27)-a(35) from Amiram Eldar, Sep 11 2019
STATUS
approved