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A271102 a(n) is multiplicative with a(p^e) = -1 if e=2, a(p^e) = 0 if e=1 or e>2. 9

%I

%S 1,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,

%T 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0

%N a(n) is multiplicative with a(p^e) = -1 if e=2, a(p^e) = 0 if e=1 or e>2.

%H Antti Karttunen, <a href="/A271102/b271102.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F Dirichlet g.f.: 1 / zeta(2*s).

%F abs(a(n)) = A227291(n).

%e G.f. = x - x^4 - x^9 - x^25 + x^36 - x^49 + x^100 - x^121 - x^169 + ...

%t Table[Times @@ Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 1 :> If[e == 2, -1, 0]], {n, 105}] (* _Michael De Vlieger_, Jul 29 2017 *)

%t Table[DivisorSum[n, Abs[MoebiusMu[#]]*MoebiusMu[n/#] &], {n, 1, 100}] (* _Vaclav Kotesovec_, Apr 08 2019 *)

%o (PARI) {a(n) = if( n<1, 0, direuler( p=2, n, 1 - X^2 )[n])};

%o (PARI) {a(n) = my(A, p, e); if( n<1, 0, A = factor(n); prod(k=1, matsize(A)[1], [p, e] = A[k, ]; -(e==2)))};

%o (Scheme) (define (A271102 n) (if (= 1 n) n (* (if (= 2 (A067029 n)) -1 0) (A271102 (A028234 n))))) ;; _Antti Karttunen_, Jul 28 2017

%Y Cf. A227291 (gives the absolute values).

%K sign,mult

%O 1

%A _Michael Somos_, Mar 30 2016

%E More terms from _Antti Karttunen_, Jul 28 2017

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)