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%I #22 Jan 20 2024 03:11:40
%S 1,-1,0,1,2,0,4,-1,0,-2,8,0,10,-4,0,1,14,0,16,2,0,-8,20,0,4,-10,0,4,
%T 26,0,28,-1,0,-14,8,0,34,-16,0,-2,38,0,40,8,0,-20,44,0,16,-4,0,10,50,
%U 0,16,-4,0,-26,56,0,58,-28,0,1,20,0,64,14,0,-8,68,0
%N Totally multiplicative sequence with a(p) = p-3 for prime p.
%H Amiram Eldar, <a href="/A166589/b166589.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = (p-3)^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)-3)^e(k). a(3k) = 0 for k >= 1. Abs (a(2^k)) = 1 for k >= 1.
%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (p*(p-1)/(p^2-p+3)) = 0.196347937547... . - _Amiram Eldar_, Jan 20 2024
%t a[1] = 1; a[p_?PrimeQ] := p-3; a[n_] := Times @@ Power @@@ ({#[[1]]-3, #[[2]]}& /@ FactorInteger[n]); Array[a, 72] (* _Jean-François Alcover_, Jul 19 2017 *)
%o (PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i,1] -=3); factorback(f); \\ _Michel Marcus_, Jun 09 2014
%Y Cf. A166586.
%K sign,easy,mult
%O 1,5
%A _Jaroslav Krizek_, Oct 17 2009
%E More terms from _Michel Marcus_, Jun 09 2014
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