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

1,1

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

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}]]

Crossrefs

Cf. A033950, A114617.

Sequence in context: A219726 A017017 A297665 * A273235 A334964 A309351

Adjacent sequences: A309344 A309345 A309346 * A309348 A309349 A309350

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 24 2019

Status

approved