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%I #11 Oct 22 2023 00:51:38
%S 1,25,30,625,40,750,50,15625,900,1000,70,18750,80,1250,1200,390625,
%T 100,22500,110,25000,1500,1750,130,468750,1600,2000,27000,31250,160,
%U 30000,170,9765625,2100,2500,2000,562500,200,2750,2400,625000,220,37500,230
%N Totally multiplicative sequence with a(p) = 5*(p+3) for prime p.
%H G. C. Greubel, <a href="/A167324/b167324.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (5*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+3))^e(k).
%F a(n) = A165826(n) * A166591(n) = 5^bigomega(n) * A166591(n) = 5^A001222(n) * A166591(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t f[p_, e_] := (5*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2023 *)
%Y Cf. A001222, A165826, A166591.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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