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

1,3

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

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}]]

Crossrefs

Cf. A033950, A309347.

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

Sequence in context: A026485 A294662 A183301 * A047318 A057904 A188397

Adjacent sequences: A308062 A308063 A308064 * A308066 A308067 A308068

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 27 2019

Status

approved