A190621 a(n) = n if n is not divisible by 4, otherwise 0.

0, 1, 2, 3, 0, 5, 6, 7, 0, 9, 10, 11, 0, 13, 14, 15, 0, 17, 18, 19, 0, 21, 22, 23, 0, 25, 26, 27, 0, 29, 30, 31, 0, 33, 34, 35, 0, 37, 38, 39, 0, 41, 42, 43, 0, 45, 46, 47, 0, 49, 50, 51, 0, 53, 54, 55, 0, 57, 58, 59, 0, 61, 62, 63, 0, 65, 66, 67, 0, 69, 70, 71, 0, 73, 74, 75, 0, 77, 78, 79, 0, 81, 82, 83, 0, 85, 86

Offset: 0

Author

N. J. A. Sloane, May 14 2011

Keywords

• nonn
• mult
• easy

Comments

The sequence is multiplicative.

References

• J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 195.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1)

Crossrefs

Cf. A008586, A057427, A166486, A046897 (Mobius Trans.).

Programs

Magma

[n mod 4 ne 0 select n else 0:n in [0..86]]; // Marius A. Burtea, Jan 13 2020

Maple

seq(op([0,i,i+1,i+2]),i=1..100,4); # Robert Israel, Jan 13 2020
# alternative
A190621 := proc(n)
    if modp(n,4) <> 0 then
        n;
    else
        0;
    end if;
end proc:
seq(A190621(n),n=0..40) ; # R. J. Mathar, May 17 2023

Mathematica

Table[If[Divisible[n,4],0,n],{n,0,90}] (* Harvey P. Dale, Jan 04 2019 *)

Formula

a(n) = n * A166486(n) = n * signum(n mod 4).

G.f.: (x + 2*x^2 + 3*x^3 + 3*x^5 + 2*x^6 + x^7)/(1 - 2*x^4 + x^8). - Robert Israel, Jan 13 2020

Dirichlet g.f.: (1-4^(1-s))*zeta(s-1). - R. J. Mathar, May 17 2023