A167294 - OEIS

%I #13 Oct 19 2023 02:16:13

%S 1,0,2,0,6,0,10,0,4,0,18,0,22,0,12,0,30,0,34,0,20,0,42,0,36,0,8,0,54,

%T 0,58,0,36,0,60,0,70,0,44,0,78,0,82,0,24,0,90,0,100,0,60,0,102,0,108,

%U 0,68,0,114,0,118,0,40,0,132,0,130,0,84,0,138,0,142,0

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

%H G. C. Greubel, <a href="/A167294/b167294.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%F a(n) = A061142(n) * A166586(n) = 2^bigomega(n) * A166586(n) = 2^A001222(n) * A166586(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 06 2016 *)

%t f[p_, e_] := (2*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)

%Y Cf. A001222, A061142, A166586.

%K nonn,easy,mult

%O 1,3

%A _Jaroslav Krizek_, Nov 01 2009