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 A348827 #13 Nov 02 2021 22:20:09 %S A348827 320000,941192,1229312,3001250,5120000,8000000,14172488,14623232, %T A348827 15059072,19668992,35701250,38614472,42762752,60236288,66724352, %U A348827 75031250,121726800,128000000,143278592,147061250,168480000,222814800,226759808,233971712,257875200,319813200 %N A348827 Nonsquare numbers k such that the denominator of the harmonic mean of the divisors of k is larger than 2*k. %C A348827 The smallest term that is not twice a square is a(17) = 121726800 = 13 * 3060^2. %H A348827 Amiram Eldar, <a href="/A348827/b348827.txt">Table of n, a(n) for n = 1..100</a> %e A348827 320000 = 2 * 400^2 is a term since it is not a square, the harmonic mean of the divisors of 320000 is 16000000/798963 and 798963 > 2*320000 = 640000. %t A348827 q[n_] := !IntegerQ @ Sqrt[n] && Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]] > 2*n; Select[Range[8000000], q] %o A348827 (PARI) isok(k) = if (!issquare(k), my(d=divisors(k)); (denominator(#d/sum(i=1, #d, 1/d[i])) > 2*k)); \\ _Michel Marcus_, Nov 01 2021 %o A348827 (PARI) list(lim)=my(v=List()); forfactored(n=320000, lim\1, if(gcd(n[2][, 2])%2 && denominator(sigma(n, 0)/sigma(n, -1))>2*n[1], listput(v, n[1]))); Vec(v) \\ _Charles R Greathouse IV_, Nov 01 2021 %Y A348827 Cf. A001105, A099377, A099378. %Y A348827 Intersection of A000037 and A348826. %Y A348827 Subsequence of A005101 and A348825. %K A348827 nonn %O A348827 1,1 %A A348827 _Amiram Eldar_, Nov 01 2021