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 A068067 #20 Sep 15 2024 02:45:57
%S A068067 1,0,2,0,2,1,2,0,2,1,2,1,2,1,4,0,2,1,2,1,4,1,2,1,2,1,2,1,2,3,2,0,4,1,
%T A068067 4,1,2,1,4,1,2,3,2,1,4,1,2,1,2,1,4,1,2,1,4,1,4,1,2,3,2,1,4,0,4,3,2,1,
%U A068067 4,3,2,1,2,1,4,1,4,3,2,1,2,1,2,3,4,1,4,1,2,3,4,1,4,1,4,1,2,1,4,1,2,3,2,1,8
%N A068067 Number of integers m, 0 < m <= n, such that n divides m(m+1)/2.
%C A068067 Least n with a(n) = 2^k is prime(k+1)#/2 = A002110(A000040(k+1))/2. Least n with a(n) = 2^k-1 != 1 is p(k+1)#.
%H A068067 G. C. Greubel, <a href="/A068067/b068067.txt">Table of n, a(n) for n = 1..10000</a>
%F A068067 a(n) = 0 iff n = 2^k with k >= 1.
%F A068067 If n is even, a(n) = 2^(omega(n)-1) - 1; if n is odd, a(n) = 2^omega(n). Here omega(n) = A001221(n) is the number of distinct prime divisors of n.
%F A068067 A068068(n) - a(n) = 0 if n is odd, 1 if n is even.
%t A068067 a[n_] := Length[Select[Range[n], Mod[ #(#+1)/2, n]==0&]]
%o A068067 (PARI) a(n) = {my(c = 0); for(k = 1, n, c += !((k*(k+1)/2) % n)); c;} \\ _Amiram Eldar_, Sep 15 2024
%Y A068067 Cf. A000040, A001221, A002110, A068068.
%K A068067 nonn
%O A068067 1,3
%A A068067 _Robert G. Wilson v_, Feb 18 2002
%E A068067 Edited by _David W. Wilson_ and _Dean Hickerson_, Jun 08 2002