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A076340 Real part of the function defined multiplicatively on the complex numbers by 2->(2,0) and p->((floor(p/4)+floor((p mod 4)/2))*4,2-(p mod 4)) for odd primes p.

%I A076340 #8 Dec 12 2021 11:51:43
%S A076340 1,2,4,4,4,8,8,8,15,8,12,16,12,16,17,16,16,30,20,16,31,24,24,32,15,24,
%T A076340 52,32,28,34,32,32,47,32,33,60,36,40,49,32,40,62,44,48,68,48,48,64,63,
%U A076340 30,65,48,52,104,49,64,79,56,60,68,60,64,112,64,47,94,68,64,95,66,72
%N A076340 Real part of the function defined multiplicatively on the complex numbers by 2->(2,0) and p->((floor(p/4)+floor((p mod 4)/2))*4,2-(p mod 4)) for odd primes p.
%C A076340 a(n)>0 for n<2187=3^7, a(2187)=-5816, A076341(2187)=-20047.
%F A076340 a(A000040(n)) = A076342(n).
%F A076340 a(A001358(n)) = A076343(n).
%F A076340 a(A000961(n)) = A076345(n).
%F A076340 a(A005117(n)) = A076347(n).
%F A076340 a(A000290(n)) = A076349(n).
%e A076340 n=21: 21 = 3*7 = (4-1)*(8-1) = (4,-1)*(8,-1) -> (32-(-1)*(-1),-4+(-8)) = (31,-12), therefore a(21)=31, A076341(21)=-12;
%e A076340 n=35: 35 = 5*7 = (4+1)*(8-1) = (4,1)*(8,-1) -> (32-1*(-1),-4+8) = (33,4), therefore a(35)=33, A076341(35)=4.
%t A076340 b[n_] := If[n == 1, 1, Product[{p, e} = pe; If[p == 2, 2, ((Floor[p/4] + Floor[Mod[p, 4]/2])*4 + (2 - Mod[p, 4]) I)]^e, {pe, FactorInteger[n]}]];
%t A076340 a[n_] := Re[b[n]];
%t A076340 Array[a, 100] (* _Jean-François Alcover_, Dec 12 2021 *)
%Y A076340 Imaginary part = A076341.
%Y A076340 Cf. A076342, A076343, A076345, A076347, A076349.
%Y A076340 Cf. A000040, A001358, A000961, A005117, A000290.
%K A076340 nonn
%O A076340 1,2
%A A076340 _Reinhard Zumkeller_, Oct 08 2002