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A340769 The third-smallest divisor of n-th square number, n>1.

%I A340769 #17 Oct 09 2024 04:36:05
%S A340769 4,9,4,25,3,49,4,9,4,121,3,169,4,5,4,289,3,361,4,7,4,529,3,25,4,9,4,
%T A340769 841,3,961,4,9,4,7,3,1369,4,9,4,1681,3,1849,4,5,4,2209,3,49,4,9,4,
%U A340769 2809,3,11,4,9,4,3481,3,3721,4,7,4,13,3,4489,4,9,4,5041,3
%N A340769 The third-smallest divisor of n-th square number, n>1.
%C A340769 The terms are either primes or squares of primes.
%H A340769 Robert Israel, <a href="/A340769/b340769.txt">Table of n, a(n) for n = 2..10000</a>
%p A340769 f:= proc(n) local F,t;
%p A340769   F:= sort(ifactors(n)[2],(a,b) -> a[1]<b[1]);
%p A340769   if nops(F) >= 2 and F[2,1] < F[1,1]^2 then F[2,1] else F[1,1]^2 fi
%p A340769 end proc:
%p A340769 map(f, [$2..100]); # _Robert Israel_, Oct 09 2024
%t A340769 a[n_] := Divisors[n^2][[3]]; Array[a, 100, 2] (* _Amiram Eldar_, Jan 20 2021 *)
%o A340769 (PARI) a(n) = divisors(n^2)[3]; \\ _Michel Marcus_, Jan 20 2021
%Y A340769 Cf. A020639, A000290, A000040, A001248, A000430.
%K A340769 nonn
%O A340769 2,1
%A A340769 _Charles Kusniec_, Jan 20 2021