A241854 Number m that give records for the quotient between the maximum and minimum x's such that sigma(x)=m.

1, 12, 42, 60, 168, 360, 744, 1512, 2418, 2880, 9360, 19344, 28800, 39312, 59520, 79248, 112320, 232128, 471744, 714240, 1451520, 1572480, 2437344, 3249792, 6604416, 9999360, 16790592, 20321280, 34122816, 40965120, 51663360, 104993280, 179988480, 302230656, 365783040

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.

Links

Table of n, a(n) for n=1..35.

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

Cf. A241852 (similar but with difference).

Sequence in context: A287152 A109275 A360961 * A085798 A335150 A270700

Adjacent sequences: A241851 A241852 A241853 * A241855 A241856 A241857

Keyword

nonn

Author

Michel Marcus, Apr 30 2014

Extensions

a(27)-a(35) from Amiram Eldar, Sep 11 2019

Status

approved