A308065 Nonnegative integers that are not the sum of two refactorable numbers whose difference is refactorable.

0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Author

Wesley Ivan Hurt, Jul 27 2019

Keywords

• nonn

Comments

Differs from A047318 (not congruent to 3 (mod 7)) starting at a(n=22) = 24 = 3*7 + 3 which is in this sequence but not in A047318. - M. F. Hasler, Jun 30 2025

Links

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

Crossrefs

Cf. A033950, A309347.

Different from A047318 (not congruent to 3 modulo 7) and A057904.

Programs

Maple

notref:= proc(n) option remember; n mod numtheory:-tau(n) <> 0 end proc:
filter:= proc(n)
  andmap(t -> notref(t) or notref(n-t) or notref(n-2*t), [$1 .. (n-1)/2])
end proc:
select(filter, [$0..100]); # 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, 0, 100}]]