A000091 Multiplicative with a(2^e) = 2 for k >= 1; a(3) = 2, a(3^e) = 0 for k >= 2; a(p^e) = 0 if p > 3 and p == -1 (mod 3); a(p^e) = 2 if p > 3 and p == 1 (mod 3).
1, 2, 2, 2, 0, 4, 2, 2, 0, 0, 0, 4, 2, 4, 0, 2, 0, 0, 2, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, 0, 0, 8, 2, 0, 0, 0, 0, 4, 2, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 2, 4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 4, 0, 8, 2, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 4, 0
Offset: 1
Links
- Christian G. Bower, Table of n, a(n) for n = 1..2000
Programs
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Maple
A000091 := proc(n) local b,d,nt,c; if n = 1 then RETURN(1); fi; c := 1; if n mod 2 = 0 then c := c*2; fi; if n mod 3 = 0 then c := c*2; fi; nt := n; while nt mod 2 = 0 do nt := nt/2; od; while nt mod 3 = 0 do nt := nt/3; od; if irem(n,9) = 0 then RETURN(0); fi; b := 1; for d from 3 to nt do if irem(nt,d) = 0 and isprime(d) then b := b*(1+legendre(-3,d)); fi; od; RETURN(b*c); end;
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Mathematica
a[1] = 1; a[n_] := Block[{b, d, nt, c = 1}, If[Mod[n, 2] == 0, c = c*2]; If[Mod[n, 3] == 0, c = c*2]; nt = n; While[ Mod[nt, 2] == 0, nt = nt/2]; While[ Mod[nt, 3] == 0, nt = nt/3]; If[Mod[n, 9] == 0, Return[0]]; b = 1; For[d = 3, d <= nt, d++, If[Mod[nt, d] == 0 && PrimeQ[d], b = b*(1+JacobiSymbol[-3, d])]]; Return[b*c]]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Feb 06 2012, after Maple *)
Extensions
Description corrected Mar 02 2004. (The old description defined A000086, not this sequence.)