A272880 Number of integers in [prime(n), 2*prime(n)] with maximal number of divisors.

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, 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, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,3

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

a[n_] := Tally[Sort@ DivisorSigma[0, Range[#, 2 #]&@ Prime@n]][[-1, 2]]; Array[a, 87] (* Giovanni Resta, May 08 2016 *)

Prog

(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

Crossrefs

Cf. A272771, A272777.

Sequence in context: A375117 A331286 A381079 * A003636 A353415 A078929

Adjacent sequences: A272877 A272878 A272879 * A272881 A272882 A272883

Keyword

nonn

Author

Vladimir Shevelev, May 08 2016

Extensions

More terms from Peter J. C. Moses, May 08 2016

Status

approved