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

Author

John W. Layman, Nov 30 2000

Keywords

• nonn

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.

Crossrefs

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

Includes 2*A124518.

Programs

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 *)