A076341 - OEIS

%I #8 Dec 12 2021 11:51:35

%S 0,0,-1,0,1,-2,-1,0,-8,2,-1,-4,1,-2,0,0,1,-16,-1,4,-12,-2,-1,-8,8,2,

%T -47,-4,1,0,-1,0,-16,2,4,-32,1,-2,-8,8,1,-24,-1,-4,-17,-2,-1,-16,-16,

%U 16,-12,4,1,-94,8,-8,-24,2,-1,0,1,-2,-79,0,16,-32,-1,4,-28,8,-1,-64,1,2,17,-4

%N Imaginary 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.

%F a(A000040(n)) = A070750(n).

%F a(A001358(n)) = A076344(n).

%F a(A000961(n)) = A076346(n).

%F a(A005117(n)) = A076348(n).

%F a(A000290(n)) = A076350(n);

%F a(A076351(n)) = 0.

%e n=21: 21 = 3*7 = (4-1)*(8-1) = (4,-1)*(8,-1) -> (32-(-1)*(-1),-4+(-8)) = (31,-12), therefore a(21)=-12, A076340(21)=31;

%e n=35: 35 = 5*7 = (4+1)*(8-1) = (4,1)*(8,-1) -> (32-1*(-1),-4+8) = (33,4), therefore a(35)=4, A076340(35)=33.

%t 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 a[n_] := Im[b[n]];

%t Array[a, 100] (* _Jean-François Alcover_, Dec 12 2021 *)

%Y Real part = A076340.

%Y Cf. A070750, A076344, A076346, A076348, A076350, A076351.

%Y Cf. A000040, A001358, A000961, A005117, A000290.

%K sign

%O 1,6

%A _Reinhard Zumkeller_, Oct 08 2002