A371012 The largest prime that divides the n-th number that is the sum of 2 squares; a(2) = 1.

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, 13, 17, 3, 73, 37, 5, 3, 41, 17, 89, 5, 97, 7, 5, 101, 13, 53, 109, 113, 29, 13, 11, 61, 5, 2, 13, 17, 137, 3, 29, 73, 37, 149, 17, 157, 5, 3, 41, 13, 17, 173, 89

Offset: 2

Author

Amiram Eldar, Mar 08 2024

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10001
• Rafael Jakimczuk, Generalizations of Mertens's Formula and k-Free and s-Full Numbers with Prime Divisors in Arithmetic Progression, ResearchGate, 2024.

Crossrefs

Cf. A001481, A006530, A344123.

Programs

Mathematica

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

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], ", ")));}

Formula

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

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).