A272771 Smallest k in the interval [prime(n), 2*prime(n)], such that k has the maximal number of divisors in this interval.

4, 6, 6, 12, 12, 24, 24, 36, 36, 48, 60, 60, 60, 60, 60, 60, 60, 120, 120, 120, 120, 120, 120, 120, 180, 180, 180, 180, 180, 180, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 360, 360, 360, 360, 360, 360

Offset

1,1

Comments

Conjecturally the different values of the sequence are highly composite numbers (A002182, n>=3).

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Example

Let n=5, prime(n)=11. In interval [11,22] we have 3 numbers 12,18 and 20 with the  maximal number of divisors in this interval(6). Since 12 is the smallest of them, then a(5)=12.

Mathematica

Table[Function[p, First@ FirstPosition[#, Max@ #] + p - 1 &@ Map[DivisorSigma[0, #] &, Range[p, 2 p]]]@ Prime@ n, {n, 80}] (* Michael De Vlieger, May 07 2016, Version 10 *)

Crossrefs

Cf. A000005, A000040.

Sequence in context: A304409 A081732 A079033 * A346675 A077038 A379445

Adjacent sequences: A272768 A272769 A272770 * A272772 A272773 A272774

Keyword

nonn

Author

Vladimir Shevelev, May 06 2016

Status

approved