A167307 - OEIS

%I #12 Oct 19 2023 02:15:50

%S 1,24,30,576,42,720,54,13824,900,1008,78,17280,90,1296,1260,331776,

%T 114,21600,126,24192,1620,1872,150,414720,1764,2160,27000,31104,186,

%U 30240,198,7962624,2340,2736,2268,518400,234,3024,2700,580608,258,38880,270

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

%H G. C. Greubel, <a href="/A167307/b167307.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(n) = A165827(n) * A166590(n) = 6^bigomega(n) * A166590(n) = 6^A001222(n) * A166590(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 19 2023 *)

%Y Cf. A001222, A165827, A166590.

%K nonn,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009