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 A351311 #24 Jul 19 2025 11:57:51
%S A351311 1,1,1,4097,1,1,1,4097,531442,1,1,4097,1,1,1,16781313,1,531442,1,4097,
%T A351311 1,1,1,4097,244140626,1,531442,4097,1,1,1,16781313,1,1,1,2177317874,1,
%U A351311 1,1,4097,1,1,1,4097,531442,1,1,16781313,13841287202,244140626,1,4097,1,531442,1
%N A351311 Sum of the 6th powers of the square divisors of n.
%C A351311 Inverse Möbius transform of n^6 * c(n), where c(n) is the characteristic function of squares (A010052). - _Wesley Ivan Hurt_, Jun 21 2024
%H A351311 Michael De Vlieger, <a href="/A351311/b351311.txt">Table of n, a(n) for n = 1..10000</a>
%F A351311 a(n) = Sum_{d^2|n} (d^2)^6.
%F A351311 Multiplicative with a(p) = (p^(12*(1+floor(e/2))) - 1)/(p^12 - 1). - _Amiram Eldar_, Feb 07 2022
%F A351311 From _Amiram Eldar_, Sep 20 2023: (Start)
%F A351311 Dirichlet g.f.: zeta(s) * zeta(2*s-12).
%F A351311 Sum_{k=1..n} a(k) ~ (zeta(13/2)/13) * n^(13/2). (End)
%F A351311 a(n) = Sum_{d|n} d^6 * c(d), where c = A010052. - _Wesley Ivan Hurt_, Jun 21 2024
%F A351311 a(n) = Sum_{d|n} lambda(d)*d^6*sigma_6(n/d), where lambda = A008836. - _Ridouane Oudra_, Jul 19 2025
%e A351311 a(16) = 16781313; a(16) = Sum_{d^2|16} (d^2)^6 = (1^2)^6 + (2^2)^6 + (4^2)^6 = 16781313.
%t A351311 f[p_, e_] := (p^(12*(1 + Floor[e/2])) - 1)/(p^12 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 07 2022 *)
%Y A351311 Sum of the k-th powers of the square divisors of n for k=0..10: A046951 (k=0), A035316 (k=1), A351307 (k=2), A351308 (k=3), A351309 (k=4), A351310 (k=5), this sequence (k=6), A351313 (k=7), A351314 (k=8), A351315 (k=9), A351315 (k=10).
%Y A351311 Cf. A010052, A008836, A013954.
%K A351311 nonn,easy,mult
%O A351311 1,4
%A A351311 _Wesley Ivan Hurt_, Feb 06 2022