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

1,2

Comments

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

Links

Table of n, a(n) for n=1..71.

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).

Example

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.

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 *)

Crossrefs

Imaginary part = A076341.

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

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

Sequence in context: A108039 A367013 A103228 * A076345 A327331 A231349

Adjacent sequences: A076337 A076338 A076339 * A076341 A076342 A076343

Keyword

nonn

Author

Reinhard Zumkeller, Oct 08 2002

Status

approved