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Totally multiplicative sequence with a(p) = 3*(p+2) for prime p.
1

%I #12 Oct 21 2023 05:34:00

%S 1,12,15,144,21,180,27,1728,225,252,39,2160,45,324,315,20736,57,2700,

%T 63,3024,405,468,75,25920,441,540,3375,3888,93,3780,99,248832,585,684,

%U 567,32400,117,756,675,36288,129,4860,135,5616,4725,900,147,311040,729,5292

%N Totally multiplicative sequence with a(p) = 3*(p+2) for prime p.

%H G. C. Greubel, <a href="/A167304/b167304.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (3*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+2))^e(k).

%F a(n) = A165824(n) * A166590(n) = 3^bigomega(n) * A166590(n) = 3^A001222(n) * A166590(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)

%t f[p_, e_] := (3*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2023 *)

%Y Cf. A001222, A165824, A166590.

%K nonn,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009