A058218 Positive integers that cannot be represented in the form n=5|ab|+a+b for any choice of nonzero integers a and b (positive or negative).

1, 2, 4, 6, 8, 10, 12, 14, 18, 22, 26, 28, 30, 32, 36, 40, 44, 48, 50, 54, 58, 60, 62, 66, 76, 78, 82, 84, 94, 96, 98, 100, 102, 104, 114, 116, 120, 126, 132, 136, 138, 140, 144, 150, 154, 158, 162, 166, 170, 176, 184, 188, 190, 198, 202, 204, 208, 210, 212, 216, 220

Offset

1,2

Comments

All terms except 1 are even. - Robert Israel, Apr 07 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maria Suzuki, Related to Alternative Formulations of the Twin Prime Problem, American Math. Monthly, 107 (2000) pp. 55-56.

Maple

filter:= proc(n)
   nops(select(t -> t mod 5 = 1 or t mod 5 = 4, numtheory:-divisors(5*n+1))) = 2
   and nops(select(t -> t mod 5 = 4, numtheory:-divisors(5*n-1)))=1
end proc:
select(filter, [$1..1000]); # Robert Israel, Apr 07 2019

Mathematica

filterQ[n_] := Length[Select[Divisors[5 n + 1], Mod[#, 5] == 1 || Mod[#, 5] == 4&]] == 2 && Length[Select[Divisors[5 n - 1], Mod[#, 5] == 4&]] == 1;
Select[Range[1000], filterQ] (* Jean-François Alcover, Aug 16 2020, after Robert Israel *)

Crossrefs

A002822 results if the coefficient 5 in the definition above is replaced by 6.

Includes 2*A124518.

Sequence in context: A098807 A189562 A194372 * A264986 A140955 A111905

Adjacent sequences: A058215 A058216 A058217 * A058219 A058220 A058221

Keyword

nonn

Author

John W. Layman, Nov 30 2000

Status

approved