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.

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, 52, 32, 28, 34, 32, 32, 47, 32, 33, 60, 36, 40, 49, 32, 40, 62, 44, 48, 68, 48, 48, 64, 63, 30, 65, 48, 52, 104, 49, 64, 79, 56, 60, 68, 60, 64, 112, 64, 47, 94, 68, 64, 95, 66, 72

Offset: 1

Author

Reinhard Zumkeller, Oct 08 2002

Keywords

• nonn

Comments

a(n)>0 for n<2187=3^7, a(2187)=-5816, A076341(2187)=-20047.

Examples

			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;
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.
		

Crossrefs

Imaginary part = A076341.

Cf. A076342, A076343, A076345, A076347, A076349.

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

Programs

Mathematica

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]}]];
a[n_] := Re[b[n]];
Array[a, 100] (* Jean-François Alcover, Dec 12 2021 *)

Formula

a(A000040(n)) = A076342(n).

a(A001358(n)) = A076343(n).

a(A000961(n)) = A076345(n).

a(A005117(n)) = A076347(n).

a(A000290(n)) = A076349(n).