A390689 The sum of the divisors of n that are sums of 2 squares (A001481).

1, 3, 1, 7, 6, 3, 1, 15, 10, 18, 1, 7, 14, 3, 6, 31, 18, 30, 1, 42, 1, 3, 1, 15, 31, 42, 10, 7, 30, 18, 1, 63, 1, 54, 6, 70, 38, 3, 14, 90, 42, 3, 1, 7, 60, 3, 1, 31, 50, 93, 18, 98, 54, 30, 6, 15, 1, 90, 1, 42, 62, 3, 10, 127, 84, 3, 1, 126, 1, 18, 1, 150, 74, 114

Offset

1,2

Comments

The number of these divisors is A371014(n) and the largest of them is A371015(n).

Links

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

Formula

a(n) = Sum_{d|n} A229062(d) * d.

Multiplicative with a(p^e) = (p^(2*(floor(e/2) + 1)) - 1)/(p^2 - 1) if p == 3 (mod 4), and (p^(e+1) - 1)/(p - 1) otherwise.

a(n) = A000203(n) if and only if n is in A072437.

a(n) = A035316(n) if and only if n is in A004614.

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

Mathematica

f[p_, e_] := If[Mod[p, 4] == 3, (p^(2*(Floor[e/2] + 1)) - 1)/(p^2 - 1), (p^(e + 1) - 1)/(p - 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 1]%4 == 3, (f[i, 1]^(2*(f[i, 2]\2 + 1)) - 1)/(f[i, 1]^2 - 1), (f[i, 1]^(f[i, 2] + 1) - 1)/(f[i, 1] - 1))); }

Crossrefs

Cf. A000203, A001481, A004614, A035316, A072437, A167181, A229062, A371014, A371015, A390690.

Sequence in context: A054458 A110168 A323663 * A355928 A205298 A046913

Adjacent sequences: A390686 A390687 A390688 * A390690 A390691 A390692

Keyword

nonn,mult,easy

Author

Amiram Eldar, Nov 15 2025

Status

approved