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%I #19 Nov 26 2017 05:29:21
%S 1,2,6,12,60,60,420,6720,20160,20160,221760,14192640,184504320,
%T 184504320,184504320,12679040325931499520,215543685540835491840,
%U 1939893169867519426560,36857970227482869104640
%N a(1) = 1; for n >= 2, suppose a(n-1) = Product p_i^e_i and n = Product p_i^f_i, then a(n) = Product p_i^(e_i*f_i).
%H Iain Fox, <a href="/A072181/b072181.txt">Table of n, a(n) for n = 1..35</a>
%F Let m = Product (p_i)^(e_{i, m}), m=1, 2, ..., where p_i is i_th prime. Then a(n) = Product_{i>=1} (p_i)^(Product_{m =1..n} (e_{i, m})).
%F Let m = Product (p_i)^(e_{i, m}), m=1, 2, ..., where p_i is i_th prime. Then a(n) = Product_{i>=1} (p_i)^(Product_{m =1..n}[max(1, e_{i, m})]). - _David Wasserman_, Sep 07 2004
%e n=12: a(11) = 221760 = 2^6 3^2 5 7 11, 12 = 2^2 3^1, so a(12) = 2^(2*6) 3^(1*1) 5 7 11 = 14192640.
%t Clear[a]; a[n_] := a[n] = (ff = Join[ FactorInteger[n] , FactorInteger[a[n - 1]]] // Sort; Times @@ Power @@@ (ff //. {x___, {p_, e_}, {p_, f_}, y___} :> {x, {p, e*f}, y})); a[1] = 1; Table[a[n], {n, 1, 19}] (* _Jean-François Alcover_, Jan 15 2013 *)
%o (PARI) step(k,n)=if(n<3, return(n)); my(f=factor(k), g=factor(n), p=Set(concat(f[,1],g[,1])), x=((f,p) -> my(i=setsearch(f[,1]~,p)); if(i,f[i,2],1)), e=apply(q->x(f,q)*x(g,q),p)); factorback(concat(Mat(p~),e~))
%o vector(20, n, k=step(k,n)) \\ _Charles R Greathouse IV_, Oct 16 2015
%K nonn,easy,nice
%O 1,2
%A _Naohiro Nomoto_, Jun 30 2002
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