A167316 - OEIS

%I #13 Oct 22 2023 00:50:49

%S 1,-6,0,36,12,0,24,-216,0,-72,48,0,60,-144,0,1296,84,0,96,432,0,-288,

%T 120,0,144,-360,0,864,156,0,168,-7776,0,-504,288,0,204,-576,0,-2592,

%U 228,0,240,1728,0,-720,264,0,576,-864,0,2160,300,0,576,-5184,0,-936,336

%N Totally multiplicative sequence with a(p) = 6*(p-3) for prime p.

%H G. C. Greubel, <a href="/A167316/b167316.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (6*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-3))^e(k).

%F a(3k) = 0 for k >= 1.

%F a(n) = A165827(n) * A166589(n) = 6^bigomega(n) * A166589(n) = 6^A001222(n) * A166589(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)

%t f[p_, e_] := (6*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)

%Y Cf. A001222, A165827, A166589.

%K sign,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009