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A371015 The largest divisor of n that is the sum of 2 squares.

%I A371015 #7 Mar 08 2024 08:09:16
%S A371015 1,2,1,4,5,2,1,8,9,10,1,4,13,2,5,16,17,18,1,20,1,2,1,8,25,26,9,4,29,
%T A371015 10,1,32,1,34,5,36,37,2,13,40,41,2,1,4,45,2,1,16,49,50,17,52,53,18,5,
%U A371015 8,1,58,1,20,61,2,9,64,65,2,1,68,1,10,1,72,73,74,25
%N A371015 The largest divisor of n that is the sum of 2 squares.
%H A371015 Amiram Eldar, <a href="/A371015/b371015.txt">Table of n, a(n) for n = 1..10000</a>
%F A371015 Multiplicative with a(p^e) = p^(2*floor(e/2)) if p == 3 (mod 4), and p^e otherwise.
%F A371015 a(n) = n / A363340(n).
%F A371015 a(n) = n if and only if n is in A001481.
%F A371015 a(n) = 1 if and only if n is in A167181.
%t A371015 f[p_, e_] := If[Mod[p, 4] == 3, p^(2*Floor[e/2]), p^e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A371015 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^if(f[i, 1]%4 == 3, 2*(f[i, 2]\2), f[i, 2]));}
%Y A371015 Cf. A001481, A167181, A363340, A371014.
%K A371015 nonn,easy,mult
%O A371015 1,2
%A A371015 _Amiram Eldar_, Mar 08 2024