The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A351647 Sum of the squares of the odd proper divisors of n. 12
 0, 1, 1, 1, 1, 10, 1, 1, 10, 26, 1, 10, 1, 50, 35, 1, 1, 91, 1, 26, 59, 122, 1, 10, 26, 170, 91, 50, 1, 260, 1, 1, 131, 290, 75, 91, 1, 362, 179, 26, 1, 500, 1, 122, 341, 530, 1, 10, 50, 651, 299, 170, 1, 820, 147, 50, 371, 842, 1, 260, 1, 962, 581, 1, 195, 1220, 1, 290 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 Index entries for sequences related to sums of divisors. FORMULA a(n) = Sum_{d|n, d=1} (2*k-1)^2 * x^(4*k-2) / (1 - x^(2*k-1)). - Ilya Gutkovskiy, Mar 02 2022 From Amiram Eldar, Oct 11 2023: (Start) a(n) = A050999(n) - n^2*A000035(n). Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(3)-1)/6 = 0.0336761505... . (End) EXAMPLE a(10) = 26; a(10) = Sum_{d|10, d<10, d odd} d^2 = 1^2 + 5^2 = 26. MATHEMATICA f[2, e_] := 1; f[p_, e_] := (p^(2*e+2) - 1)/(p^2 - 1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n^2, 0]; Array[a, 60] (* Amiram Eldar, Oct 11 2023 *) PROG (PARI) a(n) = sumdiv(n, d, if ((d%2) && (d

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 9 07:24 EDT 2024. Contains 375762 sequences. (Running on oeis4.)