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

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, 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, 8, 1, 58, 1, 20, 61, 2, 9, 64, 65, 2, 1, 68, 1, 10, 1, 72, 73, 74, 25

Offset: 1

Author

Amiram Eldar, Mar 08 2024

Keywords

• nonn
• easy
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001481, A167181, A363340, A371014.

Programs

Mathematica

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]

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]));}

Formula

Multiplicative with a(p^e) = p^(2*floor(e/2)) if p == 3 (mod 4), and p^e otherwise.

a(n) = n / A363340(n).

a(n) = n if and only if n is in A001481.

a(n) = 1 if and only if n is in A167181.