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

Author

David A. Corneth, Mar 24 2018

Keywords

• nonn

Examples

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

Crossrefs

Cf. A288814.

Programs

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 *)

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