A390141 Numbers k such that k - sopfr(k) is a positive fourth power.

1, 6, 166, 650, 4125, 4476, 13126, 28866, 50721, 101254, 194680, 194691, 197631, 388966, 391874, 392245, 401796, 883644, 933058, 1051146, 1212885, 1338556, 1345468, 1362556, 3112095, 3112338, 3229448, 3429816, 3748206, 3907208, 4100996, 4101369, 5766146, 5767652, 5774043, 6263536, 6297062

Offset

1,2

Comments

Numbers k such that A075255(k) is a positive fourth power.

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

Includes 2*p for p in A182343.

Except for 1, a subset of A386245.

Links

Robert Israel, Table of n, a(n) for n = 1..110

Example

a(3) = 166 is a term because 166 = 2*83 so A075255(166) = 166 - 2 - 83 = 81 = 3^4 is a fourth power.

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 4 = 0, ifactors(x)[2][.., 2]);
end proc:
select(filter, [$1..1000000]);

Mathematica

sopfr[k_]:=Plus @@ Times @@@ FactorInteger@ k; sopfr[1] = 0; okQ[k_]:=k-sopfr[k]>0&&IntegerQ[Surd[(k-sopfr[k]), 4]]; Select[Range[10^6], okQ] (* James C. McMahon, Oct 31 2025 *)

Prog

(PARI) isok(k) = my(f=factor(k), x=k-sum(i=1, #f~, f[i, 1]*f[i, 2])); (x>0) && ispower(x, 4); \\ Michel Marcus, Oct 27 2025

Crossrefs

Cf. A001414, A075255, A182343, A386245, A387246, A389889.

Sequence in context: A177781 A178435 A183254 * A143534 A104729 A106661

Adjacent sequences: A390138 A390139 A390140 * A390142 A390143 A390144

Keyword

nonn

Author

Will Gosnell and Robert Israel, Oct 26 2025

Status

approved