|
%I #13 Oct 19 2023 02:16:06
%S 1,0,8,0,24,0,40,0,64,0,72,0,88,0,192,0,120,0,136,0,320,0,168,0,576,0,
%T 512,0,216,0,232,0,576,0,960,0,280,0,704,0,312,0,328,0,1536,0,360,0,
%U 1600,0,960,0,408,0,1728,0,1088,0,456,0,472,0,2560,0,2112,0
%N Totally multiplicative sequence with a(p) = 8*(p-2) for prime p.
%H G. C. Greubel, <a href="/A167300/b167300.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (8*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)-2))^e(k).
%F a(2k) = 0 for k >= 1.
%F a(n) = A165829(n) * A166586(n) = 8^bigomega(n) * A166586(n) = 8^A001222(n) * A166586(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*8^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)
%t f[p_, e_] := (8*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)
%Y Cf. A001222, A165829, A166586.
%K nonn,easy,mult
%O 1,3
%A _Jaroslav Krizek_, Nov 01 2009
|
