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%I #12 Oct 22 2023 00:50:17
%S 1,-5,0,25,10,0,20,-125,0,-50,40,0,50,-100,0,625,70,0,80,250,0,-200,
%T 100,0,100,-250,0,500,130,0,140,-3125,0,-350,200,0,170,-400,0,-1250,
%U 190,0,200,1000,0,-500,220,0,400,-500,0,1250,250,0,400,-2500,0,-650,280
%N Totally multiplicative sequence with a(p) = 5*(p-3) for prime p.
%H G. C. Greubel, <a href="/A167315/b167315.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (5*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-3))^e(k).
%F a(3k) = 0 for k >= 1.
%F a(n) = A165826(n) * A166589(n) = 5^bigomega(n) * A166589(n) = 5^A001222(n) * A166589(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t f[p_, e_] := (5*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)
%Y Cf. A001222, A165826, A166589.
%K sign,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009