This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102440 #15 Feb 04 2020 03:58:56 %S A102440 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 A102440 27,24,26,24,26,32,30,30,24,36,35,30,30,32,39,36,39,40,36,44,46,48,36, %U A102440 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 A102440 Replace each prime factor of n that is greater than 3 with the greatest semiprime less than it. %H A102440 Amiram Eldar, <a href="/A102440/b102440.txt">Table of n, a(n) for n = 1..10000</a> %F A102440 Multiplicative with prime(i) -> (if i<=2 then prime(i) else A102415(i)). %F A102440 a(n) <= n and a(n) = n iff n is 3-smooth, see A003586. %F A102440 A102441(n) = a(a(n)), see A102442, A102443 for iterations. %e A102440 a(99) = a(3*3*11) -> 3*3*[11->2*5] = 3*3*2*5 = 90. %t A102440 g[p_] := (* greatest semiprime less than prime p *) g[p] = For[k = p - 1, True, k--, If[PrimeOmega[k] == 2, Return[k]]]; %t A102440 a[n_] := Product[{p, e} = pe; If[p <= 3, p, g[p]]^e, {pe, FactorInteger[n]}]; %t A102440 a /@ Range[1, 100] (* _Jean-François Alcover_, Sep 27 2019 *) %Y A102440 Cf. A102415, A102441, A102442, A102443. %K A102440 nonn,mult %O A102440 1,2 %A A102440 _Reinhard Zumkeller_, Jan 09 2005