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 A167328 Totally multiplicative sequence with a(p) = 9*(p+3) for prime p. 1

%I

%S 1,45,54,2025,72,2430,90,91125,2916,3240,126,109350,144,4050,3888,

%T 4100625,180,131220,198,145800,4860,5670,234,4920750,5184,6480,157464,

%U 182250,288,174960,306,184528125,6804,8100,6480,5904900,360,8910,7776

%N Totally multiplicative sequence with a(p) = 9*(p+3) for prime p.

%H G. C. Greubel, <a href="/A167328/b167328.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (9*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)+3))^e(k). a(n) = A165830(n) * A166591(n) = 9^bigomega(n) * A166591(n) = 9^A001222(n) * A166591(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)

%K nonn,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009

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