%I #7 Mar 08 2024 08:08:25

%S 1,2,2,5,2,3,5,13,2,17,3,5,5,13,29,2,17,3,37,5,41,5,7,5,13,53,29,61,2,

%T 13,17,3,73,37,5,3,41,17,89,5,97,7,5,101,13,53,109,113,29,13,11,61,5,

%U 2,13,17,137,3,29,73,37,149,17,157,5,3,41,13,17,173,89

%N The largest prime that divides the n-th number that is the sum of 2 squares; a(2) = 1.

%H Amiram Eldar, <a href="/A371012/b371012.txt">Table of n, a(n) for n = 2..10001</a>

%H Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.27745.48487">Generalizations of Mertens's Formula and k-Free and s-Full Numbers with Prime Divisors in Arithmetic Progression</a>, ResearchGate, 2024.

%F a(n) = A006530(A001481(n+1)).

%F Sum_{k >= 2, A001481(k) < n} a(k) = (1/4) * c * n^2/log(n) + o(n^2/log(n)), where c = A344123 (Jakimczuk, 2024, Theorem 4.9, p. 54).

%t FactorInteger[#][[-1, 1]] & /@ Select[Range[200], SquaresR[2, #] > 0 &]

%o (PARI) lista(kmax) = {my(f, is); print1(1, ", "); for(k = 2, kmax, f = factor(k); is = 1; for(i=1, #f~, if(f[i, 2]%2 && f[i, 1]%4 == 3, is = 0; break)); if(is, print1(f[#f~, 1], ", ")));}

%Y Cf. A001481, A006530, A344123.

%K nonn,easy

%O 2,2

%A _Amiram Eldar_, Mar 08 2024