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%I #15 Feb 04 2020 03:58:56
%S 1,2,3,4,4,6,6,8,9,8,10,12,10,12,12,16,15,18,15,16,18,20,22,24,16,20,
%T 27,24,26,24,26,32,30,30,24,36,35,30,30,32,39,36,39,40,36,44,46,48,36,
%U 32,45,40,51,54,40,48,45,52,58,48,58,52,54,64,40,60,65,60,66,48,69,72,69
%N Replace each prime factor of n that is greater than 3 with the greatest semiprime less than it.
%H Amiram Eldar, <a href="/A102440/b102440.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with prime(i) -> (if i<=2 then prime(i) else A102415(i)).
%F a(n) <= n and a(n) = n iff n is 3-smooth, see A003586.
%F A102441(n) = a(a(n)), see A102442, A102443 for iterations.
%e a(99) = a(3*3*11) -> 3*3*[11->2*5] = 3*3*2*5 = 90.
%t g[p_] := (* greatest semiprime less than prime p *) g[p] = For[k = p - 1, True, k--, If[PrimeOmega[k] == 2, Return[k]]];
%t a[n_] := Product[{p, e} = pe; If[p <= 3, p, g[p]]^e, {pe, FactorInteger[n]}];
%t a /@ Range[1, 100] (* _Jean-François Alcover_, Sep 27 2019 *)
%Y Cf. A102415, A102441, A102442, A102443.
%K nonn,mult
%O 1,2
%A _Reinhard Zumkeller_, Jan 09 2005
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