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%I #12 Oct 18 2023 02:09:49
%S 1,40,50,1600,70,2000,90,64000,2500,2800,130,80000,150,3600,3500,
%T 2560000,190,100000,210,112000,4500,5200,250,3200000,4900,6000,125000,
%U 144000,310,140000,330,102400000,6500,7600,6300,4000000,390,8400,7500
%N Totally multiplicative sequence with a(p) = 10*(p+2) for prime p.
%H G. C. Greubel, <a href="/A167311/b167311.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(n) = A165831(n) * A166590(n) = 10^bigomega(n) * A166590(n) = 10^A001222(n) * A166590(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 18 2023 *)
%Y Cf. A001222, A165831, A166590.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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