A309347 Sums of two refactorable numbers whose difference is refactorable.

3, 10, 17, 27, 36, 48, 54, 60, 84, 88, 96, 104, 108, 112, 120, 128, 132, 136, 144, 152, 156, 168, 176, 180, 184, 192, 200, 204, 208, 216, 224, 228, 232, 240, 248, 252, 256, 264, 272, 276, 280, 288, 296, 300, 304, 312, 324, 328, 336, 344, 348, 352, 360, 368

Offset: 1

Author

Wesley Ivan Hurt, Jul 24 2019

Keywords

• nonn

Comments

Includes k+2 for k in A114617. - Robert Israel, Jul 29 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Refactorable Number

Crossrefs

Cf. A033950, A114617.

Programs

Maple

isref:= proc(n) option remember; n mod numtheory:-tau(n) = 0 end proc:
filter:= proc(n)
  ormap(t -> isref(t) and isref(n-t) and isref(n-2*t), [$1 .. (n-1)/2])
end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 29 2025

Mathematica

Flatten[Table[If[Sum[ (1 - Ceiling[(n - 2 i)/DivisorSigma[0, n - 2 i]] + Floor[(n - 2 i)/DivisorSigma[0, n - 2 i]]) (1 - Ceiling[i/DivisorSigma[0, i]] + Floor[i/DivisorSigma[0, i]]) (1 - Ceiling[(n - i)/DivisorSigma[0, n - i]] + Floor[(n - i)/DivisorSigma[0, n - i]]), {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 400}]]