login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A050461
a(n) = Sum_{d|n, n/d=1 mod 4} d^2.
7
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
1,2
COMMENTS
Not multiplicative: a(3)*a(7) <> a(21), for example. - R. J. Mathar, Dec 20 2011
LINKS
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)
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 *)
PROG
(Haskell)
a050461 n = sum [d ^ 2 | d <- a027750_row n, mod (div n d) 4 == 1]
-- Reinhard Zumkeller, Mar 06 2012
(PARI) a(n) = sumdiv(n, d, (n/d % 4 == 1) * d^2); \\ Amiram Eldar, Nov 05 2023
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 23 1999
STATUS
approved