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 A000091 Multiplicative with a(2^k) = 2 for k >= 1; a(3) = 2, a(3^k) = 0 for k >= 2; a(p) = 0 if p >3 and p == -1 mod 3; a(p) = 2 if p > 3 and p == 1 mod 3. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Christian G. Bower, Table of n, a(n) for n=1..2000 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; 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 *) CROSSREFS Sequence in context: A091399 A263527 A261444 * A155123 A125938 A215461 Adjacent sequences:  A000088 A000089 A000090 * A000092 A000093 A000094 KEYWORD nonn,easy,mult AUTHOR EXTENSIONS Description corrected Mar 02 2004. (The old description defined A000086, not this sequence.) STATUS approved

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