%I #11 Oct 22 2023 00:50:28
%S 1,-10,0,100,20,0,40,-1000,0,-200,80,0,100,-400,0,10000,140,0,160,
%T 2000,0,-800,200,0,400,-1000,0,4000,260,0,280,-100000,0,-1400,800,0,
%U 340,-1600,0,-20000,380,0,400,8000,0,-2000,440,0,1600,-4000,0,10000,500,0,1600
%N Totally multiplicative sequence with a(p) = 10*(p-3) for prime p.
%H G. C. Greubel, <a href="/A167320/b167320.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (10*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-3))^e(k).
%F a(3k) = 0 for k >= 1.
%F a(n) = A165831(n) * A166589(n) = 10^bigomega(n) * A166589(n) = 10^A001222(n) * A166589(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*10^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t f[p_, e_] := (10*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)
%Y Cf. A001222, A165831, A166589.
%K sign,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009