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%I #12 Oct 19 2023 02:15:53
%S 1,20,25,400,35,500,45,8000,625,700,65,10000,75,900,875,160000,95,
%T 12500,105,14000,1125,1300,125,200000,1225,1500,15625,18000,155,17500,
%U 165,3200000,1625,1900,1575,250000,195,2100,1875,280000,215,22500,225,26000
%N Totally multiplicative sequence with a(p) = 5*(p+2) for prime p.
%H G. C. Greubel, <a href="/A167306/b167306.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (5*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+2))^e(k).
%F a(n) = A165826(n) * A166590(n) = 5^bigomega(n) * A166590(n) = 5^A001222(n) * A166590(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)
%t f[p_, e_] := (5*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)
%Y Cf. A001222, A165826, A166590.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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