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 A351313 #23 Jul 19 2025 12:30:22
%S A351313 1,1,1,16385,1,1,1,16385,4782970,1,1,16385,1,1,1,268451841,1,4782970,
%T A351313 1,16385,1,1,1,16385,6103515626,1,4782970,16385,1,1,1,268451841,1,1,1,
%U A351313 78368963450,1,1,1,16385,1,1,1,16385,4782970,1,1,268451841,678223072850,6103515626,1
%N A351313 Sum of the 7th powers of the square divisors of n.
%C A351313 Inverse Möbius transform of n^7 * c(n), where c(n) is the characteristic function of squares (A010052). - _Wesley Ivan Hurt_, Jun 21 2024
%H A351313 Michael De Vlieger, <a href="/A351313/b351313.txt">Table of n, a(n) for n = 1..10000</a>
%F A351313 a(n) = Sum_{d^2|n} (d^2)^7.
%F A351313 Multiplicative with a(p) = (p^(14*(1+floor(e/2))) - 1)/(p^14 - 1). - _Amiram Eldar_, Feb 07 2022
%F A351313 From _Amiram Eldar_, Sep 20 2023: (Start)
%F A351313 Dirichlet g.f.: zeta(s) * zeta(2*s-14).
%F A351313 Sum_{k=1..n} a(k) ~ (zeta(15/2)/15) * n^(15/2). (End)
%F A351313 a(n) = Sum_{d|n} d^7 * c(d), where c = A010052. - _Wesley Ivan Hurt_, Jun 21 2024
%F A351313 a(n) = Sum_{d|n} lambda(d)*d^7*sigma_7(n/d), where lambda = A008836. - _Ridouane Oudra_, Jul 19 2025
%e A351313 a(16) = 268451841; a(16) = Sum_{d^2|16} (d^2)^7 = (1^2)^7 + (2^2)^7 + (4^2)^7 = 268451841.
%t A351313 f[p_, e_] := (p^(14*(1 + Floor[e/2])) - 1)/(p^14 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 07 2022 *)
%Y A351313 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), A351311 (k=6), this sequence (k=7), A351314 (k=8), A351315 (k=9), A351315 (k=10).
%Y A351313 Cf. A010052, A008836, A013955.
%K A351313 nonn,easy,mult
%O A351313 1,4
%A A351313 _Wesley Ivan Hurt_, Feb 06 2022