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 A145191 #23 Sep 22 2024 04:32:48
%S A145191 1,20,68,903,3876,3890,19096,19122,19127,110990,111004,111007,111010,
%T A145191 111013,774276,774277,774278,774279,774303,774313,774314,774315,
%U A145191 6615593,70607550,70607559,959878582,959878737,959878753,959878836,959878846,959878888,959878902,959878914
%N A145191 Numbers m such that Sum_{i=1..m} omega(i)^2 is divisible by m, where omega is A001221.
%C A145191 If for some m is c square, then we have RootMeanSquare(omega(1),...,omega(n)) = c.
%t A145191 With[{max = 10^5}, Position[Accumulate[PrimeNu[Range[max]]^2]/Range[max], _?IntegerQ] // Flatten] (* _Amiram Eldar_, Sep 22 2024 *)
%o A145191 (PARI) isok(m) = !frac(sum(i=1, m, omega(i)^2)/m); \\ _Michel Marcus_, Mar 15 2022
%o A145191 (PARI) lista(nn) = {my(v = vector(nn, k, omega(k)^2)); print1(1, ", "); for (n=2, nn, v[n] += v[n-1]; if (! frac(v[n]/n), print1(n, ", ")););} \\ _Michel Marcus_, Mar 16 2022
%o A145191 (PARI) listaa(nn) = {my(v = vector(nn, k, omega(k)^2)); print1(1, ", "); for (n=2, nn, v[n] += v[n-1]; if (! frac(v[n]/n), print1(n, ", "));); for (m=1, 100, last = v[nn]; v = vector(nn, k, omega(k+m*nn)^2); v[1] += last; for (n=2, nn, v[n] += v[n-1]; if (! frac(v[n]/(m*nn+n)), print1(n+m*nn, ", "));););} \\ _Michel Marcus_, Mar 16 2022
%Y A145191 Cf. A001221, A063971, A013939, A140480.
%K A145191 nonn
%O A145191 1,2
%A A145191 _Ctibor O. Zizka_, Oct 03 2008
%E A145191 a(7)-a(9) from _Michel Marcus_, Mar 15 2022
%E A145191 a(10)-a(25) from _Michel Marcus_, Mar 16 2022
%E A145191 a(26)-a(33) from _Amiram Eldar_, Sep 22 2024