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

1,2

Links

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

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

Example

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.

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 *)

Prog

(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

Crossrefs

Sequence in context: A109935 A347304 A065887 * A283487 A126915 A328450

Adjacent sequences: A072178 A072179 A072180 * A072182 A072183 A072184

Keyword

nonn,easy,nice

Author

Naohiro Nomoto, Jun 30 2002

Status

approved