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%I #14 Sep 20 2020 04:23:11
%S 1,10,18,100,40,180,70,1000,324,400,154,1800,208,700,720,10000,340,
%T 3240,418,4000,1260,1540,598,18000,1600,2080,5832,7000,928,7200,1054,
%U 100000,2772,3400,2800,32400,1480,4180,3744,40000,1804,12600,1978,15400,12960
%N Totally multiplicative sequence with a(p) = p*(p+3) = p^2+3p for prime p.
%H G. C. Greubel, <a href="/A167342/b167342.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (p*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)+3))^e(k). a(n) = n * A166591(n).
%F Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 3*p - 1)) = 1.256741057020447773244230946716370792268447699628630376844295183469512964116... - _Vaclav Kotesovec_, Sep 20 2020
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* _G. C. Greubel_, Jun 10 2016 *)
%K nonn,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009