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%I #18 Dec 15 2022 06:15:54
%S 1,0,0,0,6,0,20,0,0,0,72,0,110,0,0,0,210,0,272,0,0,0,420,0,36,0,0,0,
%T 702,0,812,0,0,0,120,0,1190,0,0,0,1482,0,1640,0,0,0,1980,0,400,0,0,0,
%U 2550,0,432,0,0,0,3192,0,3422,0,0,0,660,0,4160,0,0,0
%N Totally multiplicative sequence with a(p) = (p-2)*(p-3) = p^2-5p+6 for prime p.
%H G. C. Greubel, <a href="/A167356/b167356.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = ((p-2)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-2)*(p(k)-3))^e(k).
%F a(2k) = 0 for k >= 1, a(3k) = 0 for k >= 1.
%F a(n) = A166586(n) * A166589(n).
%F Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 4/p^2 - 1/p^3 - 6/p^4) = 0.073139277512... . - _Amiram Eldar_, Dec 15 2022
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 11 2016 *)
%Y Cf. A166586, A166589.
%K nonn,mult
%O 1,5
%A _Jaroslav Krizek_, Nov 01 2009
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