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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.
13
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
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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

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Last modified December 13 21:46 EST 2024. Contains 378731 sequences.
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