A272777 In the interval [prime(n), 2*prime(n)], the greatest k with the maximal number of divisors.

4, 6, 10, 12, 20, 24, 30, 36, 36, 48, 60, 72, 72, 84, 90, 96, 108, 120, 120, 120, 120, 120, 120, 168, 180, 180, 180, 180, 180, 180, 240, 240, 240, 240, 240, 240, 240, 240, 240, 336, 336, 360, 360, 360, 360, 360, 420, 420, 420, 420

Offset

1,1

Comments

The different values of the sequence are union of highly composite numbers (A002182, n>=3) and the numbers {10, 20, 30, 72, 84, 90, 96, 108, 168, 336, 420,...}.

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 20 is the most of them, then a(5)=20.

Mathematica

Table[First@ MaximalBy[Reverse@ Range[Prime@ n, 2 Prime@ n], DivisorSigma[0, #] &], {n, 50}] (* Michael De Vlieger, May 09 2016, Version 10 *)

Prog

(PARI) a(n) = {my(nb = 2*prime(n) - prime(n) + 1, vd = vector(nb, i, numdiv(prime(n)+i-1)), vmax = vecmax(vd), k = nb); while (vd[k] != vmax, k--); k+prime(n)-1; } \\ Michel Marcus, May 07 2016

Crossrefs

Cf. A000005, A000040, A002182, A272771.

Sequence in context: A310580 A353966 A073161 * A310581 A310582 A177929

Adjacent sequences: A272774 A272775 A272776 * A272778 A272779 A272780

Keyword

nonn

Author

Vladimir Shevelev, May 06 2016

Status

approved