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 A343527 #24 Jun 13 2021 13:21:44 %S A343527 1,15,239,3823,60735,972191,15517679,248252879,3969108895,63506982943, %T A343527 1015951568815,16255093526239,260068569617727,4161109496115135, %U A343527 66577084386669199,1065232436999055375,17043668344393625999,272698739815301095247,4363176901343767529551,69810828455823683068415,1116973047989955380768527 %N A343527 Number of ordered quadruples (w, x, y, z) with gcd(w, x, y, z) = 1 and 1 <= {w, x, y, z} <= 2^n. %H A343527 Chai Wah Wu, <a href="/A343527/b343527.txt">Table of n, a(n) for n = 0..52</a> (n = 0..31 from Karl-Heinz Hofmann) %F A343527 Lim_{n->infinity} a(n)/2^(4*n) = 1/zeta(4) = A215267 = 90/Pi^4. %F A343527 a(n) = A082540(2^n). %e A343527 . %e A343527 For n=3, the size of the gris is 8 X 8 X 8 X 8: %e A343527 . %e A343527 o------------x(w=8)-------------o %e A343527 /|. ./ | %e A343527 / |. ./ | %e A343527 / |. ./ | %e A343527 / |. ./ | %e A343527 / |. z(w=8) | %e A343527 / |. . / | %e A343527 / |. . / | %e A343527 / |. . / y(w=8) %e A343527 o------------------------------.o | %e A343527 |\ /|¯¯¯¯¯¯x(w=1)¯¯¯¯¯¯/. | | %e A343527 | w / | /.| | | %e A343527 | \ z(w=1)| /. | | | %e A343527 | \ / |y(w=1) /. | | | %e A343527 | \/-------------------/. | | | %e A343527 | | | | | | w | sums %e A343527 | | Cube at w = 1 | | | | ----+----- %e A343527 | | 8 X 8 X 8 | _ _| |---------o 1 | 512 %e A343527 | | contains | / | / 2 | 448 %e A343527 | | 512 | / | / 3 | 504 %e A343527 | | completely | / | / 4 | 448 %e A343527 | | reduced fractions | / | / 5 | 511 %e A343527 | | |/ | / 6 | 441 %e A343527 | /------------------- \ | / 7 | 511 %e A343527 | / \ | / 8 | 448 %e A343527 | w w | / ----+----- %e A343527 | / \ | / sum for a(3) | 3823 %e A343527 | / \ |/ %e A343527 o -------------------------------o %o A343527 (Python) %o A343527 from labmath import mobius %o A343527 def A343527(n): return sum(mobius(k)*(2**n//k)**4 for k in range(1, 2**n+1)) %Y A343527 Cf. A018805, A342632, A342586, A071778. %Y A343527 Cf. A342935, A342841, A082540, A343193. %K A343527 nonn %O A343527 0,2 %A A343527 _Karl-Heinz Hofmann_, Apr 18 2021 %E A343527 Edited by _N. J. A. Sloane_, Jun 13 2021