A241854 - OEIS

%I #10 Sep 11 2019 06:58:31

%S 1,12,42,60,168,360,744,1512,2418,2880,9360,19344,28800,39312,59520,

%T 79248,112320,232128,471744,714240,1451520,1572480,2437344,3249792,

%U 6604416,9999360,16790592,20321280,34122816,40965120,51663360,104993280,179988480,302230656,365783040

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

%C 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.

%e Only sigma(1)=1, hence the quotient is 1.

%e The next m is 12 with sigma(6)=sigma(11)=12, quotient 11/6 greater than 1.

%e Next m is 42 with [20, 26, 41] with quotient 41/20 that is greater than 11/6.

%o (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;);););}

%Y Cf. A241852 (similar but with difference).

%K nonn

%O 1,2

%A _Michel Marcus_, Apr 30 2014

%E a(27)-a(35) from _Amiram Eldar_, Sep 11 2019