A072181 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).

1, 2, 6, 12, 60, 60, 420, 6720, 20160, 20160, 221760, 14192640, 184504320, 184504320, 184504320, 12679040325931499520, 215543685540835491840, 1939893169867519426560, 36857970227482869104640

Offset: 1

Author

Naohiro Nomoto, Jun 30 2002

Keywords

• nonn
• easy
• nice

Examples

			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.
		

Links

• Iain Fox, Table of n, a(n) for n = 1..35

Programs

Mathematica

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 *)

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~))
vector(20, n, k=step(k,n)) \\ Charles R Greathouse IV, Oct 16 2015

Formula

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})).

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