A117213 a(n) = smallest term of sequence A002110 divisible by n-th squarefree positive integer.

1, 2, 6, 30, 6, 210, 30, 2310, 30030, 210, 30, 510510, 9699690, 210, 2310, 223092870, 30030, 6469693230, 30, 200560490130, 2310, 510510, 210, 7420738134810, 9699690, 30030, 304250263527210, 210, 13082761331670030, 223092870

Offset: 1

Author

Leroy Quet, Mar 03 2006

Keywords

• nonn

Examples

			10 is the 7th squarefree integer. And 2*3*5 = 30 is the smallest primorial number divisible by 10 = 2*5. So a(7) = 30.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1441

Crossrefs

Cf. A002110, A073482, A117214.

Programs

Maple

issquarefree := proc(n::integer) local nf, ifa, lar ; nf := op(2,ifactors(n)) ; for ifa from 1 to nops(nf) do lar := op(1,op(ifa,nf)) ; if op(2,op(ifa,nf)) >= 2 then RETURN(0) ; fi ; od : RETURN(lar) ; end: primor := proc(n::integer) local resul, nepr ; resul :=2 ; nepr :=3 ; while nepr <= n do resul := resul*nepr ; nepr:=nextprime(nepr) ; od : RETURN(resul) ; end: printf("1,") ; for n from 2 to 100 do lfa := issquarefree(n) ; if lfa > 0 then printf("%a,",primor(lfa) ) ; fi ; od : # R. J. Mathar, Apr 02 2006

Mathematica

Select[Array[Which[# == 1, 1, SquareFreeQ@ #, Product[Prime@ i, {i, PrimePi@ FactorInteger[#][[-1, 1]]}], True, 0] &, 50], # > 0 & ] (* Michael De Vlieger, Sep 30 2017 *)

Formula

For n >= 2, a(n) = product of the primes <= A073482(n).

Extensions

More terms from R. J. Mathar, Apr 02 2006