|
%I #12 May 09 2016 03:18:28
%S 1,1,3,1,3,1,2,1,1,1,1,2,2,3,4,5,6,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,
%T 1,1,1,1,1,2,2,1,1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,5,5,5,5,5,6,6,6,7,8,9,
%U 9,9,9,9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N Number of integers in [prime(n), 2*prime(n)] with maximal number of divisors.
%H Giovanni Resta, <a href="/A272880/b272880.txt">Table of n, a(n) for n = 1..10000</a>
%e Let n=3, prime(n)=5. In the interval [5,10] we have 3 numbers {6,8,10} with maximal number of divisors in this interval (4). So, a(3)=3.
%t a[n_] := Tally[Sort@ DivisorSigma[0, Range[#,2 #]&@ Prime@n]][[-1, 2]]; Array[a, 87] (* _Giovanni Resta_, May 08 2016 *)
%o (PARI) a(n) = {my(nb = 2*prime(n) - prime(n) + 1); my(vd = vector(nb, i, numdiv(prime(n)+i-1))); my(vmax = vecmax(vd)); #select(x->x == vmax, vd);} \\ _Michel Marcus_, May 09 2016
%Y Cf. A272771, A272777.
%K nonn
%O 1,3
%A _Vladimir Shevelev_, May 08 2016
%E More terms from _Peter J. C. Moses_, May 08 2016
|
