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A301592 Numbers k at which the ratio A288814(k) / k reaches a record high. 0
4, 5, 6, 7, 8, 10, 11, 12, 17, 18, 24, 28, 29, 37, 53, 59, 67, 79, 89, 95, 97, 121, 123, 125, 223, 305, 329, 479, 521, 539, 541, 905, 1087, 1147, 1277, 1345, 1351, 1355, 1357, 5779, 8923, 10003, 11773, 12883, 19371, 19651, 19657, 28277, 31445 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

A288814(10) / 10 = 21 / 10 and for n < 10 all ratios are less than 21 / 10, so 10 is in the sequence.

MATHEMATICA

Block[{s = Array[If[PrimeQ@ #, 0, Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger@ #]] &, 10^5, 2], t}, t = Table[(1 + FirstPosition[s, k][[1]])/k, {k, 4, LengthWhile[Differences@ Rest@ Union@ s, # == 1 &]}]; Map[3 + FirstPosition[t, #][[1]] &, Union@ FoldList[Max, t]]] (* Michael De Vlieger, Mar 26 2018 *)

PROG

(PARI) isok(k, n) = my(f=factor(k)); sum(j=1, #f~, f[j, 1]*f[j, 2]) == n;

f(n) = forcomposite(k=1, , if (isok(k, n), return(k))); /* A288814 */

lista(nn) = {maxr = 0; for (n=4, nn, if ((newr=f(n)/n) > maxr, print1(n, ", "); maxr = newr); ); } \\ Michel Marcus, Mar 26 2018

CROSSREFS

Cf. A288814.

Sequence in context: A231369 A251392 A076597 * A194414 A182204 A121541

Adjacent sequences:  A301589 A301590 A301591 * A301593 A301594 A301595

KEYWORD

nonn

AUTHOR

David A. Corneth, Mar 24 2018

STATUS

approved

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Last modified May 7 22:52 EDT 2021. Contains 343652 sequences. (Running on oeis4.)