A259749 Numbers that are congruent to {1,2,5,7,10,11,13,17,19,23} mod 24.

1, 2, 5, 7, 10, 11, 13, 17, 19, 23, 25, 26, 29, 31, 34, 35, 37, 41, 43, 47, 49, 50, 53, 55, 58, 59, 61, 65, 67, 71, 73, 74, 77, 79, 82, 83, 85, 89, 91, 95, 97, 98, 101, 103, 106, 107, 109, 113, 115, 119, 121, 122, 125, 127, 130, 131, 133, 137, 139, 143, 145

Offset: 1

Author

José María Grau Ribas, Jul 04 2015

Keywords

• nonn
• easy

Comments

Original name: Numbers n such that A259748(n) = 0.

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-2,2,-1).

Crossrefs

Cf. A000914.

Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259750, A259751, A259752, A259754, A259755.

Programs

Mathematica

A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #]  == 0 & ]
Rest@ CoefficientList[Series[x (1 + x^2) (1 + 2 x^2 - x^3 + 2 x^4 - 2 x^5 + 3 x^6 + x^7)/((1 - x)^2*(1 - x + x^2 - x^3 + x^4) (1 + x + x^2 + x^3 + x^4)), {x, 0, 61}], x] (* Michael De Vlieger, Aug 25 2016 *)
Select[Range[150],MemberQ[{1,2,5,7,10,11,13,17,19,23},Mod[#,24]]&] (* or *) LinearRecurrence[{2,-2,2,-2,2,-2,2,-2,2,-1},{1,2,5,7,10,11,13,17,19,23},70] (* Harvey P. Dale, Jan 15 2022 *)

PARI

Vec(x*(1+x^2)*(1+2*x^2-x^3+2*x^4-2*x^5+3*x^6+x^7)/((1-x)^2*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)) + O(x^100)) \\ Colin Barker, Aug 25 2016

Formula

A259748(a(n)) = Sum_{x*y: x,y in Z/a(n)Z, x<>y} = 0.

G.f.: x*(1+x^2)*(1+2*x^2-x^3+2*x^4-2*x^5+3*x^6+x^7) / ((1-x)^2*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)). - Colin Barker, Aug 25 2016

Extensions

Better name from Danny Rorabaugh, Oct 22 2015