A167298 - OEIS

%I #14 Oct 28 2023 04:05:21

%S 1,0,6,0,18,0,30,0,36,0,54,0,66,0,108,0,90,0,102,0,180,0,126,0,324,0,

%T 216,0,162,0,174,0,324,0,540,0,210,0,396,0,234,0,246,0,648,0,270,0,

%U 900,0,540,0,306,0,972,0,612,0,342,0,354,0,1080,0,1188,0,390

%N Totally multiplicative sequence with a(p) = 6*(p-2) for prime p.

%H G. C. Greubel, <a href="/A167298/b167298.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (6*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-2))^e(k).

%F a(2k) = 0 for k >= 1.

%F a(n) = A165827(n) * A166586(n) = 6^bigomega(n) * A166586(n) = 6^A001222(n) * A166586(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)

%t f[p_, e_] := (6*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 28 2023 *)

%Y Cf. A001222, A165827, A166586.

%K nonn,easy,mult

%O 1,3

%A _Jaroslav Krizek_, Nov 01 2009