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A272777 In the interval [prime(n), 2*prime(n)], the greatest k with the maximal number of divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A122171 A310580 A073161 * A310581 A310582 A177929

Adjacent sequences:  A272774 A272775 A272776 * A272778 A272779 A272780

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 06 2016

STATUS

approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)