A050461 a(n) = Sum_{d|n, n/d=1 mod 4} d^2.

1, 4, 9, 16, 26, 36, 49, 64, 82, 104, 121, 144, 170, 196, 234, 256, 290, 328, 361, 416, 442, 484, 529, 576, 651, 680, 738, 784, 842, 936, 961, 1024, 1090, 1160, 1274, 1312, 1370, 1444, 1530, 1664, 1682, 1768, 1849, 1936, 2132, 2116, 2209

Offset: 1

Author

N. J. A. Sloane, Dec 23 1999

Keywords

• nonn
• easy

Comments

Not multiplicative: a(3)*a(7) <> a(21), for example. - R. J. Mathar, Dec 20 2011

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050465, A050470, A076577, A027750, A002117.

Cf. A050460, A050462, A050463.

Programs

Haskell

a050461 n = sum [d ^ 2 | d <- a027750_row n, mod (div n d) 4 == 1]
-- Reinhard Zumkeller, Mar 06 2012

Maple

A050461 := proc(n)
        a := 0 ;
        for d in numtheory[divisors](n) do
                if (n/d) mod 4 = 1 then
                        a := a+d^2 ;
                end if;
        end do:
        a;
end proc:
seq(A050461(n),n=1..40) ; # R. J. Mathar, Dec 20 2011

Mathematica

a[n_] := DivisorSum[n, Boole[Mod[n/#, 4] == 1]*#^2&]; Array[a, 50] (* Jean-François Alcover, Feb 12 2018 *)

PARI

a(n) = sumdiv(n, d, (n/d % 4 == 1) * d^2); \\ Amiram Eldar, Nov 05 2023

Formula

a(n) = A050470(n) + A050465(n). - Reinhard Zumkeller, Mar 06 2012

From Amiram Eldar, Nov 05 2023: (Start)

a(n) = A076577(n) - A050465(n).

a(n) = (A050470(n) + A076577(n))/2.

Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = Pi^3/64 + 7*zeta(3)/16 = 1.010372968262... . (End)