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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.

A355544 Numbers k such that the arithmetic mean of the first k squarefree numbers is an integer.

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%I A355544 #10 Jul 07 2022 02:07:43
%S A355544 1,3,6,37,75,668,1075,37732,742767,1811865,3140083,8937770,108268896,
%T A355544 282951249,633932500,1275584757,60455590365
%N A355544 Numbers k such that the arithmetic mean of the first k squarefree numbers is an integer.
%C A355544 Numbers k such that A173143(k) is divisible by k.
%C A355544 The corresponding quotients A173143(k)/k are 1, 2, 4, 29, ..., and the corresponding values of A005117(k) are 1, 3, 7, 59, ... (see the link for more values).
%H A355544 Amiram Eldar, <a href="/A355544/a355544.txt">Table of n, a(n), A173143(a(n))/a(n), A005117(a(n)) for n = 1..16</a>.
%e A355544 3 is a term since the arithmetic mean of the first 3 squarefree numbers, (1+2+3)/3 = 2, is an integer.
%t A355544 s = Select[Range[10^6], SquareFreeQ]; r = Accumulate[s]/Range[Length[s]]; ind = Position[r, _?IntegerQ] // Flatten
%o A355544 (PARI) upto(n) = my(s=0,k=0); forsquarefree(m=1, n, s+=m[1]; k+=1; if(s%k == 0, print1(k, ", "))); \\ _Daniel Suteu_, Jul 06 2022
%Y A355544 Cf. A005117, A173143.
%Y A355544 Similar sequences: A045345, A050226, A056550, A064605, A064606, A064607, A064610, A064611, A064612, A048290.
%K A355544 nonn,more
%O A355544 1,2
%A A355544 _Amiram Eldar_, Jul 06 2022
%E A355544 a(17) from _Daniel Suteu_, Jul 06 2022