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

1,2

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: A350951 A263527 A261444 * A155123 A125938 A215461

Adjacent sequences: A000088 A000089 A000090 * A000092 A000093 A000094

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Extensions

Description corrected Mar 02 2004. (The old description defined A000086, not this sequence.)

Status

approved