A301592 Numbers k at which the ratio A288814(k) / k reaches a record high.

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

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 A343916

Adjacent sequences: A301589 A301590 A301591 * A301593 A301594 A301595

Keyword

nonn

Author

David A. Corneth, Mar 24 2018

Status

approved