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%I #23 May 17 2023 03:57:38
%S 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,
%T 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,
%U 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
%N a(n) = n if n is not divisible by 4, otherwise 0.
%C The sequence is multiplicative.
%D 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.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1)
%F a(n) = n * A166486(n) = n * signum(n mod 4).
%F 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
%F Dirichlet g.f.: (1-4^(1-s))*zeta(s-1). - _R. J. Mathar_, May 17 2023
%p seq(op([0,i,i+1,i+2]),i=1..100,4); # _Robert Israel_, Jan 13 2020
%p # alternative
%p A190621 := proc(n)
%p if modp(n,4) <> 0 then
%p n;
%p else
%p 0;
%p end if;
%p end proc:
%p seq(A190621(n),n=0..40) ; # _R. J. Mathar_, May 17 2023
%t Table[If[Divisible[n,4],0,n],{n,0,90}] (* _Harvey P. Dale_, Jan 04 2019 *)
%o (Magma) [n mod 4 ne 0 select n else 0:n in [0..86]]; // _Marius A. Burtea_, Jan 13 2020
%Y Cf. A008586, A057427, A166486, A046897 (Mobius Trans.).
%K nonn,mult,easy
%O 0,3
%A _N. J. A. Sloane_, May 14 2011
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