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 A385738 #12 Jul 13 2025 16:44:33
%S A385738 1,1,6,6,8,5,6,23,5,22,50,26,28,65,119,145,26,349,282,375,280,404,278,
%T A385738 369,279,370,277,276,369,378,389,378,389,15,389,13,12,210,10,9,8,210,
%U A385738 6,212,421,209,419,3,2,1,378,419,421,418,418,1026,373,105,104
%N A385738 For n >= 1, a(n) is the least k such that the Sum_{i=0..(n-1)} (k+i)/A000005(k+i) is an integer or a(n) = -1 if no such k exists.
%e A385738 For n = 4: Sum_{i=0..3} (k+i)/A000005(k+i) is an integer for the least k = 6 because 6/A000005(6) + 7/A000005(7) + 8/A000005(8) + 9/A000005(9) = 10.
%t A385738 seq[max_] := Module[{v = Table[n/DivisorSigma[0, n], {n, 1, max}], k = 1, s = {}, i}, While[NumberQ[i = FirstPosition[Plus @@@ Partition[v, k, 1], _?IntegerQ][[1]]], AppendTo[s, i]; k++]; s]; seq[1200] (* _Amiram Eldar_, Jul 08 2025 *)
%o A385738 (PARI) a(n) = my(k=1); while(denominator(sum(i=0, n-1, (k+i)/numdiv(k+i))) != 1, k++); k; \\ _Michel Marcus_, Jul 08 2025
%Y A385738 Cf. A000005.
%K A385738 nonn
%O A385738 1,3
%A A385738 _Ctibor O. Zizka_, Jul 08 2025