%I #12 Oct 21 2023 05:33:23
%S 1,0,5,0,15,0,25,0,25,0,45,0,55,0,75,0,75,0,85,0,125,0,105,0,225,0,
%T 125,0,135,0,145,0,225,0,375,0,175,0,275,0,195,0,205,0,375,0,225,0,
%U 625,0,375,0,255,0,675,0,425,0,285,0,295,0,625,0,825,0,325,0,525
%N Totally multiplicative sequence with a(p) = 5*(p-2) for prime p.
%H G. C. Greubel, <a href="/A167297/b167297.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (5*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-2))^e(k).
%F a(2k) = 0 for k >= 1.
%F a(n) = A165826(n) * A166586(n) = 5^bigomega(n) * A166586(n) = 5^A001222(n) * A166586(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)
%t f[p_, e_] := (5*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2023 *)
%Y Cf. A001222, A165826, A166586.
%K nonn,easy,mult
%O 1,3
%A _Jaroslav Krizek_, Nov 01 2009