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 A117213 a(n) = smallest term of sequence A002110 divisible by n-th squarefree positive integer. 2

%I

%S 1,2,6,30,6,210,30,2310,30030,210,30,510510,9699690,210,2310,

%T 223092870,30030,6469693230,30,200560490130,2310,510510,210,

%U 7420738134810,9699690,30030,304250263527210,210,13082761331670030,223092870

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

%H Michael De Vlieger, <a href="/A117213/b117213.txt">Table of n, a(n) for n = 1..1441</a>

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

%e 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.

%p 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

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

%Y Cf. A002110, A073482, A117214.

%K nonn

%O 1,2

%A _Leroy Quet_, Mar 03 2006

%E More terms from _R. J. Mathar_, Apr 02 2006

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Last modified July 23 17:41 EDT 2021. Contains 346259 sequences. (Running on oeis4.)