cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A069289 Sum of odd divisors of n <= sqrt(n).

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%I A069289 #14 Apr 04 2020 21:24:49
%S A069289 1,1,1,1,1,1,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,1,1,4,6,1,4,1,1,9,1,1,4,1,
%T A069289 6,4,1,1,4,6,1,4,1,1,9,1,1,4,8,6,4,1,1,4,6,8,4,1,1,9,1,1,11,1,6,4,1,1,
%U A069289 4,13,1,4,1,1,9,1,8,4,1,6,13,1,1,11,6,1,4,1
%N A069289 Sum of odd divisors of n <= sqrt(n).
%C A069289 a(n) = Sum{d : d = A182469(n,k), d <= A000196(n), k=1..A001227(n)}. - _Reinhard Zumkeller_, Apr 05 2015
%H A069289 Reinhard Zumkeller, <a href="/A069289/b069289.txt">Table of n, a(n) for n = 1..10000</a>
%F A069289 G.f.: Sum_{k>=1} (2*k - 1) * x^((2*k - 1)^2) / (1 - x^(2*k - 1)). - _Ilya Gutkovskiy_, Apr 04 2020
%t A069289 Table[Total[Select[Divisors[n],OddQ[#]&&#<=Sqrt[n]&]],{n,120}] (* _Harvey P. Dale_, Jul 16 2017 *)
%o A069289 (PARI) a(n) = my(ir = sqrtint(n)); sumdiv(n, d, (d % 2) * (d <= ir) * d); \\ _Michel Marcus_, Jan 14 2014
%o A069289 (Haskell)
%o A069289 a069289 n = sum $ takeWhile (<= a000196 n) $ a182469_row n
%o A069289 -- _Reinhard Zumkeller_, Apr 05 2015
%Y A069289 Cf. A000593, A000203, A069288.
%Y A069289 Cf. A000196, A182469, A001227.
%K A069289 nonn
%O A069289 1,9
%A A069289 _Reinhard Zumkeller_, Mar 14 2002