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%I #13 Nov 20 2020 04:52:46
%S 1,2,3,2,5,3,7,2,3,5,11,3,13,7,5,2,17,3,19,2,7,11,23,3,5,13,3,2,29,5,
%T 31,2,11,17,7,3,37,19,13,2,41,3,43,2,5,23,47,3,7,5,17,2,53,3,11,2,19,
%U 29,59,3,61,31,7,2,13,3,67,2,23,7,71,3,73,37,5,2,11,3,79,2,3,41,83,3,17,43,29
%N a(n) = the largest divisor of n such that this and every smaller divisor of n are all coprime to each other.
%C a(n) = a prime for every n >= 2.
%e The divisors of 28 are 1,2,4,7,14,28. Since 4 is not coprime with 2, but 2 is coprime with 1, then a(28) = 2.
%p with(numtheory): a:= proc(n) local l, j, s, h, k; l:= sort([divisors(n)[]]); s:= nops(l); for k while k<=s do h:= k; for j from k+1 to s do if igcd(l[k], l[j])=1 then h:=j else break fi od; s:= h od; l[s] end: seq(a(n), n=1..100); # _Alois P. Heinz_, Aug 04 2009
%t a[n_] := Module[{l = Divisors[n], j, s, h, k}, s = Length[l]; For[k = 1, k <= s, k++, h = k; For[j = k + 1, j <= s, j++, If[GCD[l[[k]], l[[j]]] == 1, h = j, Break[]]]; s = h]; l[[s]]];
%t Array[a, 100] (* _Jean-François Alcover_, Nov 20 2020, after _Alois P. Heinz_ *)
%K nonn
%O 1,2
%A _Leroy Quet_, Jul 01 2009, Jul 23 2009
%E More terms from _Alois P. Heinz_, Aug 04 2009
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