A389889 Numbers k such that k - sopfr(k) is a positive cube.

1, 6, 16, 58, 172, 254, 360, 519, 1528, 1561, 1755, 1776, 2772, 3582, 4125, 4476, 9606, 12403, 12863, 14203, 16228, 22268, 24522, 29835, 44691, 45277, 48782, 50688, 52410, 57172, 57896, 74155, 85894, 89254, 104766, 106339, 107561, 112616, 118002, 125404, 130966, 133406, 155739, 166582, 170152

Offset

1,2

Comments

Numbers k such that A075255(k) is a positive cube.

We require that the cube be positive, otherwise all primes would be terms.

Includes 2*p for p in A144953.

Links

Robert Israel, Table of n, a(n) for n = 1..1500

Example

a(3) = 16 is a term because 16 = 2^4 and 16 - 4*2 = 8 = 2^3.

Maple

filter:= proc(n) local x, t;
  x:= n - add(t[1]*t[2], t = ifactors(n)[2]);
  x > 0 and andmap(t -> t mod 3 = 0, ifactors(x)[2][.., 2]);
end proc:
select(filter, [$1..200000]);

Mathematica

sopfr[k_] := Plus @@ Times @@@ FactorInteger@ k; sopfr[1] = 0; okQ[k_]:=Module[{m=CubeRoot[k-sopfr[k]]}, !PrimeQ[k]&&IntegerQ[m]&&Positive[m]]; Select[Range[170152], okQ] (* James C. McMahon, Oct 27 2025 *)

Crossrefs

Cf. A001414, A075255, A144953, A389862.

Sequence in context: A084057 A163302 A223028 * A091649 A125628 A078672

Adjacent sequences: A389886 A389887 A389888 * A389890 A389891 A389892

Keyword

nonn

Author

Will Gosnell and Robert Israel, Oct 18 2025

Status

approved