A076341 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.

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

Offset

1,6

Links

Table of n, a(n) for n=1..76.

Formula

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

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

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

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

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

a(A076351(n)) = 0.

Example

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;
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.

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

Crossrefs

Real part = A076340.

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

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

Sequence in context: A075615 A195284 A351263 * A110510 A337506 A327363

Adjacent sequences: A076338 A076339 A076340 * A076342 A076343 A076344

Keyword

sign

Author

Reinhard Zumkeller, Oct 08 2002

Status

approved