A167302 - OEIS

%I #13 Oct 19 2023 02:15:57

%S 1,0,10,0,30,0,50,0,100,0,90,0,110,0,300,0,150,0,170,0,500,0,210,0,

%T 900,0,1000,0,270,0,290,0,900,0,1500,0,350,0,1100,0,390,0,410,0,3000,

%U 0,450,0,2500,0,1500,0,510,0,2700,0,1700,0,570,0,590,0,5000,0,3300

%N Totally multiplicative sequence with a(p) = 10*(p-2) for prime p.

%H G. C. Greubel, <a href="/A167302/b167302.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (10*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-2))^e(k).

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

%F a(n) = A165831(n) * A166586(n) = 10^bigomega(n) * A166586(n) = 10^A001222(n) * A166586(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*10^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)

%t f[p_, e_] := (10*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)

%Y Cf. A001222, A165831, A166586.

%K nonn,easy,mult

%O 1,3

%A _Jaroslav Krizek_, Nov 01 2009