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%I #17 Oct 28 2022 07:14:33
%S 1,205,5905,52429,375601,1210525,5649505,13421773,38742049,76998205,
%T 212601841,309593245,810932305,1158148525,2217923905,3435973837,
%U 6951703105,7942120045,16936647121,19692384829,33360327025,43583377405,78163228705,79255569565,146719125601
%N a(n) = sigma_4(n^4)/sigma_2(n^4).
%C sigma_y(n^x) divides sigma_x(n^x) for all n if y divides x.
%H Amiram Eldar, <a href="/A077457/b077457.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001159(n^4)/A001157(n^4).
%F Multiplicative with a(p^e) = (p^(8*e+2) + 1)/(p^2 + 1). - _Amiram Eldar_, Sep 09 2020
%F Sum_{k=1..n} a(k) ~ c * n^9, where c = (zeta(9)/9) * Product_{p prime} (1 - 1/p^3 + 1/p^5 - 1/p^7) = 0.09549806119... . - _Amiram Eldar_, Oct 28 2022
%t f[p_, e_] := (p^(8*e+2) + 1)/(p^2 + 1); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 25] (* _Amiram Eldar_, Sep 09 2020 *)
%o (PARI) a(n)=sumdiv(n^4,d,d^4)/sumdiv(n^4,d,d^2)
%o (PARI) a(n) = my(f=factor(n^4)); sigma(f, 4)/sigma(f, 2); \\ _Michel Marcus_, Sep 09 2020
%Y Cf. A001157, A001159, A013667, A057660, A077454, A077455, A077456.
%K nonn,easy,mult
%O 1,2
%A _Benoit Cloitre_, Nov 30 2002
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