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Totally multiplicative sequence with a(p) = 5*(p-2) for prime p.
1

%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