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.
%I A339009 #20 Feb 16 2025 08:34:01
%S A339009 1,2,165,170,1274,9437,69720,69732,69734,69736,515230,515236,515246,
%T A339009 28132043,28132063,28132079
%N A339009 Numbers k such that the average number of odd divisors of {1..k} is an integer.
%C A339009 Numbers k that divide A060831(k) where A060831(k) = Sum_{j=1..k} A001227(j).
%C A339009 The sequence also includes: 83860580242, 4578632504347, 4578632504465, 4578632504515. - _Daniel Suteu_, Nov 24 2020
%H A339009 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OddDivisorFunction.html">Odd Divisor Function</a>.
%e A339009 165 is in the sequence because the average number of odd divisors of {1..165} is an integer: A060831(165) / 165 = 495 / 165 = 3.
%t A339009 s[n_] := Module[{c = 0, k = 1, sum = 0, seq = {}}, While[c < n, sum += DivisorSigma[0, k/2^IntegerExponent[k, 2]]; If[Divisible[sum, k], c++; AppendTo[seq, k]]; k++]; seq]; s[13] (* _Amiram Eldar_, Nov 18 2020 *)
%o A339009 (PARI) f(n) = my(n2=n\2); sum(k=1, sqrtint(n), n\k)*2-sqrtint(n)^2-sum(k=1, sqrtint(n2), n2\k)*2+sqrtint(n2)^2; \\ A060831
%o A339009 isok(k) = (f(k) % k) == 0; \\ _Michel Marcus_, Nov 25 2020
%Y A339009 Cf. A001227, A048290, A050226, A060831, A063971, A064610, A064612.
%K A339009 nonn,more
%O A339009 1,2
%A A339009 _Ilya Gutkovskiy_, Nov 18 2020