A167341 - OEIS

%I #17 Dec 15 2022 06:16:57

%S 1,-2,0,4,10,0,28,-8,0,-20,88,0,130,-56,0,16,238,0,304,40,0,-176,460,

%T 0,100,-260,0,112,754,0,868,-32,0,-476,280,0,1258,-608,0,-80,1558,0,

%U 1720,352,0,-920,2068,0,784,-200

%N Totally multiplicative sequence with a(p) = p*(p-3) = p^2-3p for prime p.

%H G. C. Greubel, <a href="/A167341/b167341.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (p*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-3))^e(k).

%F a(3k) = 0 for k >= 1.

%F a(n) = n * A166589(n).

%F Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 2/p^2 + 3/p^3) = 0.06544931251... . - _Amiram Eldar_, Dec 15 2022

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* _G. C. Greubel_, Jun 10 2016 *)

%Y Cf. A166589.

%K sign,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009